Showing papers in "Nonlinear Dynamics in 2021"
TL;DR: In this article, the authors analyzed the one-lump-multi-stripe and soliton solutions to nonlinear partial differential equations via Hirota bilinear forms and provided necessary and sufficient conditions for the two types of interaction solutions, respectively.
Abstract: Interaction solutions between lump and soliton are analytical exact solutions to nonlinear partial differential equations. The explicit expressions of the interaction solutions are of value for analysis of the interacting mechanism. We analyze the one-lump-multi-stripe and one-lump-multi-soliton solutions to nonlinear partial differential equations via Hirota bilinear forms. The one-lump-multi-stripe solutions are generated from the combined solution of quadratic functions and N exponential functions, while the one-lump-multi-soliton solutions from the combined solution of quadratic functions and N hyperbolic cosine functions. Within the context of the derivation of the lump solution and soliton solution, necessary and sufficient conditions are presented for the two types of interaction solutions, respectively, based on the combined solutions to the associated bilinear equations. Applications are made for a (2+1)-dimensional generalized KdV equation, the (2+1)-dimensional NNV system and the (2+1)-dimensional Ito equation.
160 citations
TL;DR: This paper proposes a new color image encryption algorithm (CIEA) that sufficiently considers the properties of the color image and Latin square and designs a two-dimensional chaotic system called 2D-LSM to address the weaknesses of existing chaotic systems.
Abstract: Recently, many image encryption schemes have been developed using Latin squares. When encrypting a color image, these algorithms treat the color image as three greyscale images and encrypt these greyscale images one by one using the Latin squares. Obviously, these algorithms do not sufficiently consider the inner connections between the color image and Latin square and thus result in many redundant operations and low efficiency. To address this issue, in this paper, we propose a new color image encryption algorithm (CIEA) that sufficiently considers the properties of the color image and Latin square. First, we propose a two-dimensional chaotic system called 2D-LSM to address the weaknesses of existing chaotic systems. Then, we design a new CIEA using orthogonal Latin squares and 2D-LSM. The proposed CIEA can make full use of the inherent connections of the orthogonal Latin squares and color image and executes the encryption process in the pixel level. Simulation and security analysis results show that the proposed CIEA has a high level of security and can outperform some representative image encryption algorithms.
112 citations
TL;DR: In this article, a new extended Kadomtsev-Petviashvili (eKP) equation was developed and the Painleve analysis was used to confirm the integrability of the eKP equation.
Abstract: In this paper, we develop a new extended Kadomtsev–Petviashvili (eKP) equation We use the Painleve analysis to confirm the integrability of the eKP equation We derive the bilinear form, multiple soliton solutions and lump solutions via using the Hirota’s direct method Moreover, the soliton, breather and lump interaction solutions for this model are also obtained as well Graphs are drawn to illustrate the abundant dynamical behaviors of the obtained solutions
110 citations
TL;DR: In this paper, the authors used the physics-informed neural network to solve a variety of femtosecond optical soliton solutions of the high-order nonlinear Schrodinger equation.
Abstract: We use the physics-informed neural network to solve a variety of femtosecond optical soliton solutions of the high-order nonlinear Schrodinger equation, including one-soliton solution, two-soliton solution, rogue wave solution, W-soliton solution and M-soliton solution. The prediction error for one-soliton, W-soliton and M-soliton is smaller. As the prediction distance increases, the prediction error will gradually increase. The unknown physical parameters of the high-order nonlinear Schrodinger equation are studied by using rogue wave solutions as data sets. The neural network is optimized from three aspects including the number of layers of the neural network, the number of neurons, and the sampling points. Compared with previous research, our error is greatly reduced. This is not a replacement for the traditional numerical method, but hopefully to open up new ideas.
104 citations
TL;DR: In this paper, the authors analyzed the nonlinear forced vibration of thin-walled metal foam cylindrical shells reinforced with functionally graded graphene platelets and found that the inclusion of graphene platelet in the shells weakens the non-linear coupling effect.
Abstract: In the present study, we analyze the nonlinear forced vibration of thin-walled metal foam cylindrical shells reinforced with functionally graded graphene platelets. Attention is focused on the 1:1:1:2 internal resonances, which is detected to exist in this novel nanocomposite structure. Three kinds of porosity distribution and different kinds of graphene platelet distribution are considered. The equations of motion and the compatibility equation are deduced according to the Donnell’s nonlinear shell theory. The stress function is introduced, and then, the four-degree-of-freedom nonlinear ordinary differential equations (ODEs) are obtained via the Galerkin method. The numerical analysis of nonlinear forced vibration responses is presented by using the pseudo-arclength continuation technique. The present results are validated by comparison with those in existing literature for special cases. Results demonstrate that the amplitude–frequency relations of the system are very complex due to the 1:1:1:2 internal resonances. Porosity distribution and graphene platelet (GPL) distribution influence obviously the nonlinear behavior of the shells. We also found that the inclusion of graphene platelets in the shells weakens the nonlinear coupling effect. Moreover, the effects of the porosity coefficient and GPL weight fraction on the nonlinear dynamical response are strongly related to the porosity distribution as well as graphene platelet distribution.
98 citations
TL;DR: The basic definition of chaotic dynamics is introduced and several traditional artificial neuron and neural network models with different biological function mechanisms are reviewed, categorizing them into five types: memristive autapse neuron,memristive synapse-coupled bi-neuron network, Memristive synaptic weight neural network, neuron under electromagnetic radiation, and Neural network under electromagnetic Radiation.
Abstract: The study of dynamics on artificial neurons and neuronal networks is of great significance to understand brain functions and develop neuromorphic systems. Recently, memristive neuron and neural network models offer great potential in the investigation of neurodynamics. Many chaotic dynamics including chaos, transient chaos, hyperchaos, coexisting attractors, multistability, and extreme multistability have been researched based on the memristive neurons and neural networks. In this review, we firstly introduce the basic definition of chaotic dynamics and review several traditional artificial neuron and neural network models. Then we categorize memristive neuron and neural network models with different biological function mechanisms into five types: memristive autapse neuron, memristive synapse-coupled bi-neuron network, memristive synaptic weight neural network, neuron under electromagnetic radiation, and neural network under electromagnetic radiation. The modeling mechanisms of each type are explained and described in detail. Furthermore, the pioneer works and some recent important papers related to those types are introduced. Finally, some open problems in this field are presented to further explore future work.
98 citations
TL;DR: In this article, the neural network model of test function for the (3+1)-dimensional Jimbo-Miwa equation is extended to the 4-2-3 model by giving some specific activation functions.
Abstract: It is well known that most classical test functions to solve nonlinear partial differential equations can be constructed via single hidden layer neural network model by using Bilinear Neural Network Method (BNNM). In this paper, the neural network model of test function for the (3+1)-dimensional Jimbo–Miwa equation is extended to the “4-2-3” model. By giving some specific activation functions, new test function is constructed to obtain analytical solutions of the (3+1)-dimensional Jimbo–Miwa equation. Rogue wave solutions and the bright and dark solitons are obtained by giving some specific parameters. Via curve plots, three-dimensional plots, contour plots and density plots, dynamical characteristics of these waves are exhibited.
95 citations
TL;DR: In this article, a step function and a porosity volume fraction are introduced to describe the porosities in functionally graded material (FGM) sandwich cylindrical shells with porosity on an elastic substrate.
Abstract: The nonlinear forced vibrations of functionally graded material (FGM) sandwich cylindrical shells with porosities on an elastic substrate are studied. A step function and a porosity volume fraction are introduced to describe the porosities in FGM layers of sandwich shells. Using the Donnell’s nonlinear shallow shell theory and Hamilton’s principle, an energy approach is employed to gain the nonlinear equations of motion. Afterwards, the multi-degree-of-freedom nonlinear ordinary differential equations are carried out by using Galerkin scheme, and subsequently the pseudo-arclength continuation method is utilized to perform the bifurcation analysis. Finally, the effects of the core-to-thickness ratio, porosity volume fraction, power-law exponent, and external excitation on nonlinear forced vibration characteristics of FGM sandwich shells with porosities are investigated in detail.
91 citations
TL;DR: In this article, a model of the impulsive reaction-diffusion neural networks with infinite distributed delays is reformulated in terms of an abstract impulsive functional differential equation in Hilbert space and the local existence of the mild solution on impulsive time interval is proven by the Picard sequence and semigroup theory.
Abstract: In this paper, we focus on the global existence–uniqueness and input-to-state stability of the mild solution of impulsive reaction–diffusion neural networks with infinite distributed delays. First, the model of the impulsive reaction–diffusion neural networks with infinite distributed delays is reformulated in terms of an abstract impulsive functional differential equation in Hilbert space and the local existence–uniqueness of the mild solution on impulsive time interval is proven by the Picard sequence and semigroup theory. Then, the diffusion–dependent conditions for the global existence–uniqueness and input-to-state stability are established by the vector Lyapunov function and M-matrix where the infinite distributed delays are handled by a novel vector inequality. It shows that the ISS properties can be retained for the destabilizing impulses if there are no too short intervals between the impulses. Finally, three numerical examples verify the effectiveness of the theoretical results and that the reaction–diffusion benefits the input-to-state stability of the neural-network system.
87 citations
TL;DR: In this article, a chaotic cloud quantum bat algorithm (CCQBA) is proposed to improve the performance of BA by using a 3D cat mapping chaotic disturbance mechanism to increase population diversity.
Abstract: The bat algorithm (BA) has fast convergence, a simple structure, and strong search ability. However, the standard BA has poor local search ability in the late evolution stage because it references the historical speed; its population diversity also declines rapidly. Moreover, since it lacks a mutation mechanism, it easily falls into local optima. To improve its performance, this paper develops a hybrid approach to improving its evolution mechanism, local search mechanism, mutation mechanism, and other mechanisms. First, the quantum computing mechanism (QCM) is used to update the searching position in the BA to improve its global convergence. Secondly, the X-condition cloud generator is used to help individuals with better fitness values to increase the rate of convergence, with the sorting of individuals after a particular number of iterations; the individuals with poor fitness values are used to implement a 3D cat mapping chaotic disturbance mechanism to increase population diversity and thereby enable the BA to jump out of a local optimum. Thus, a hybrid optimization algorithm—the chaotic cloud quantum bats algorithm (CCQBA)—is proposed. To test the performance of the proposed CCQBA, it is compared with alternative algorithms. The evaluation functions are nine classical comparative functions. The results of the comparison demonstrate that the convergent accuracy and convergent speed of the proposed CCQBA are significantly better than those of the other algorithms. Thus, the proposed CCQBA represents a better method than others for solving complex problems.
85 citations
TL;DR: In this paper, the (2+1)-dimensional generalized coupled nonlinear Schrodinger equation with the four-wave mixing (FWM) term is studied, which describes the optical solitons in a birefringent fiber.
Abstract: The (2+1)-dimensional generalized coupled nonlinear Schrodinger equation with the four-wave mixing (FWM) term is studied in this paper, which describes the optical solitons in a birefringent fiber. By virtue of the Hirota method, the one- and two-soliton solutions are derived. On the basis of solutions obtained, we discuss how the values of the FWM and some free parameters affect the solitons’ peformance. The FWM parameter can help to control the amplitude of the solitons. Meanwhile, by setting the values of certain free parameters, we can control the solitons’ propagation direction and speed, and reduce the interactions between them as well. In addition, the energy transfer of solitons during elastic collision and separation is also discussed. The conclusions here may be useful in improving the communication quality in multi-mode fibers.
TL;DR: In this article, the variable coefficients fifth-order nonlinear Schrodinger equation (NLS), which can be used to describe the transmission of femtosecond pulse in the optical fiber, is studied.
Abstract: Optical fiber communication has developed rapidly because of the needs of the information age. Here, the variable coefficients fifth-order nonlinear Schrodinger equation (NLS), which can be used to describe the transmission of femtosecond pulse in the optical fiber, is studied. By virtue of the Hirota method, we get the one-soliton and two-soliton solutions. Interactions between solitons are presented, and the soliton stability is discussed through adjusting the values of dispersion and nonlinear effects. Results may potentially be useful for optical communications such as all-optical switches or the study of soliton control.
TL;DR: A new four-dimensional dissipative chaotic system which can produce multiple asymmetric attractors is designed and its dynamical behaviors are analyzed and the basin of attraction reveals the asymmetric multistability of the system.
Abstract: In this paper, a new four-dimensional dissipative chaotic system which can produce multiple asymmetric attractors is designed and its dynamical behaviors are analyzed. The basin of attraction reveals the asymmetric multistability of the system. In addition, it is very interesting to observe different types of asymmetric coexisting attractors as the bifurcation parameters change. The spectral entropy complexity chaotic diagrams are used to observe the changes in the sequence complexity when the two bifurcation parameters change simultaneously. Moreover, the difference of the system complexity between the two different initial values is analyzed. In order to facilitate engineering applications, the offset boosting control is introduced to the state variable, and the numerical simulation shows that the offset boosting control scheme can flexibly change the polarity of the chaotic signal. Finally, an analog circuit and a digital circuit were designed to verify the new chaotic system. The new research results will enrich the theoretical basis of multistability, offset boosting control and circuit implementation of chaos.
TL;DR: Performance evaluations demonstrate that the S-box generated by the proposed method has a high security level and can outperform several state-of-the-art encryption algorithms.
Abstract: Since a substitution box (S-box) is the nonlinearity part of a symmetric key encryption scheme, it directly determines the performance and security level of the encryption scheme. Thus, generating S-box with high performance and efficiency is attracting. This paper proposes a novel method to construct S-box using the complete Latin square and chaotic system. First, a complete Latin square is generated using the chaotic sequences produced by a chaotic system. Then an S-box is constructed using the complete Latin square. Performance analyses show that the S-box generated by our proposed method has a high performance and can achieve strong ability to resist many security attacks such as the linear attack, differential attack and so on. To show the efficiency of the constructed S-box, this paper further applies the S-box to image encryption application. Security analyses show that the developed image encryption algorithm is able to encrypt different kinds of images into cipher images with uniformly distributed histograms. Performance evaluations demonstrate that it has a high security level and can outperform several state-of-the-art encryption algorithms.
TL;DR: In this paper, a bilinear Backlund transformation was used to construct a (3+1)-dimensional nonlinear evolution equation, which was proposed and analyzed to study features and properties of nonlinear dynamics in higher dimensions.
Abstract: Under investigation in this paper is a (3+1)-dimensional nonlinear evolution equation, which was proposed and analyzed to study features and properties of nonlinear dynamics in higher dimensions. Using the Hirota bilinear method, we construct a bilinear Backlund transformation, which consists of four equations and involves six free parameters. With test function method and symbolic computation, three sets of lump–kink solutions and new types of interaction solutions are derived, and figures are presented to reveal the interaction behaviors. Setting constraints to the new interaction solution via the test function expressed by “polynomial-cos-cosh,” we simulate the periodic interaction phenomenon. Pfaffian solutions to the (3+1)-dimensional nonlinear evolution equation are obtained based on a set of linear partial differential conditions. According to our results, the diversity of solutions to the (3+1)-dimensional nonlinear evolution equation is revealed.
TL;DR: The main feature of this algorithm is that the robust chaos-based keystream and encryption process are highly sensitive to the plaintext, which will effectively resist against chosen-plain text and known-plaintext attacks.
Abstract: This paper introduces an image encryption algorithm shorted as CITSPD, manipulated by circle index table scrambling and partition diffusion Firstly, the circle index table is obtained through the generation, circle shift and transposition of the benchmark sequence Secondly, the plain image is transformed into the wavelet coefficient and is then scrambled by the circle index table Thirdly, the permutated image is disturbed by different noises and is further divided into four subsections Finally, the forward and inverse partition diffusions are performed to the subsections for getting the cipher image The main feature of this algorithm is that the robust chaos-based keystream and encryption process are highly sensitive to the plaintext, which will effectively resist against chosen-plaintext and known-plaintext attacks In addition, the encryption scheme is free of noise attack since the inverse diffusion differs from the forward one And the diffusion effect can be effectively enhanced by, as much as possible, increasing the small pixel value and decreasing the large pixel value Experimental tests and security analyses are carried out to verify the advantages of the scheme
TL;DR: In this article, a two-stage epidemic model with a dynamic control strategy is proposed to describe the spread of Corona Virus Disease 2019 (COVID-19) in China, and the authors investigate the appropriate control strategies to minimize the control cost and ensure the normal operation of society under the premise of containing the epidemic.
Abstract: In this paper, a novel two-stage epidemic model with a dynamic control strategy is proposed to describe the spread of Corona Virus Disease 2019 (COVID-19) in China Combined with local epidemic control policies, an epidemic model with a traceability process is established We aim to investigate the appropriate control strategies to minimize the control cost and ensure the normal operation of society under the premise of containing the epidemic This work mainly includes: (i) propose the concept about the first and the second waves of COVID-19, as well as study the case data and regularity of four cities; (ii) derive the existence and stability of the equilibrium, the parameter sensitivity of the model, and the existence of the optimal control strategy; (iii) carry out the numerical simulation associated with the theoretical results and construct a dynamic control strategy and verify its feasibility
TL;DR: In this article, a three-soliton solution for solving the coupled nonlinear Schrodinger equations is presented, and the condition for forming all-optical logic devices (AOLDs) is discussed.
Abstract: The all-optical logic device is the key component in the all-optical communication system and all-optical computing. The research based on the all-optical logic device is important to improve the communication efficiency. In this paper, using optical solitons, all-optical logic devices are investigated theoretically. Three-soliton solutions are presented through solving the coupled nonlinear Schrodinger equations. The condition for forming all-optical logic devices (AOLDs) is discussed. Besides, the performance of the AOLD is analyzed. Results of this paper have theoretical research significance for the application of the AOLD.
TL;DR: In this paper, a fractional-order multistable locally active memristor is proposed for the first time, which has infinitely many coexisting pinched hysteresis loops under different initial states and wide locally active regions.
Abstract: Fractional calculus is closer to reality and has the same memory characteristics as memristor. Therefore, a fractional-order multistable locally active memristor is proposed for the first time in this paper, which has infinitely many coexisting pinched hysteresis loops under different initial states and wide locally active regions. Through the theoretical and numerical analysis, it is found that the fractional-order memristor has stronger locally active and memory characteristics and wider nonvolatile ranges than the integer-order memristor. Furthermore, this fractional-order memristor is applied in a chaotic system. It is found that oscillations occur only within the locally active regions. This chaotic system not only has complex and rich nonlinear dynamics such as infinitely many discrete equilibrium points, multistability and anti-monotonicity but also produces two new phenomena that have not been found in other chaotic systems. The first one is transient transition: the behavior of local chaos and local period transition alternately occurring. The second is state jump: the behavior of local period-4 oscillation or local chaotic oscillation jumping to local period-2 oscillation. Finally, the circuit simulation of the fractional-order multistable locally active memristive chaotic system using PSIM is carried out to verify the validity of the numerical simulation results.
TL;DR: In this paper, a locally active memristor with coexisting two stable pinched hysteresis loops and two local activity regions is proposed, and its nonvolatile memory, as well as locally active characteristics, is validated by the power-off plot and DC V-I plot.
Abstract: Local activity is regarded as the origin of complexity. In this study, a locally active memristor with coexisting two stable pinched hysteresis loops and two local activity regions is proposed. Its nonvolatile memory, as well as locally active characteristics, is validated by the power-off plot and DC V–I plot. Based on two-dimensional Hindmarsh–Rose and two-dimensional Fitzhugh–Nagumo neurons, a simple neural network is constructed by connecting the two neurons with the locally active memristor. Coexisting multiple firing patterns under different initial conditions are investigated by considering the coupling strength as a unique controlled parameter. The results suggest that the system exhibits coexisting periodic and chaotic bursting firing patterns as well as coexisting two periodic firing patterns with different topologies. Furthermore, state switching without parameters is also explored. In particular, phase synchronization of the memristor synapse-coupled neurons is discussed, which implies that two nonidentical neurons gradually become phase synchronized with the increase in the coupling strength. In order to confirm the effectiveness of numerical simulations, circuit simulations are included.
TL;DR: Based on the doubly interval-censored data model, Wang et al. as discussed by the authors estimate the parameters of the incubation period of COVID-19 by adopting the maximum likelihood estimation, expectation maximization algorithm and a newly proposed algorithm (expectation mostly conditional maximization, referred as ECIMM).
Abstract: With the spread of the novel coronavirus disease 2019 (COVID-19) around the world, the estimation of the incubation period of COVID-19 has become a hot issue. Based on the doubly interval-censored data model, we assume that the incubation period follows lognormal and Gamma distribution, and estimate the parameters of the incubation period of COVID-19 by adopting the maximum likelihood estimation, expectation maximization algorithm and a newly proposed algorithm (expectation mostly conditional maximization algorithm, referred as ECIMM). The main innovation of this paper lies in two aspects: Firstly, we regard the sample data of the incubation period as the doubly interval-censored data without unnecessary data simplification to improve the accuracy and credibility of the results; secondly, our new ECIMM algorithm enjoys better convergence and universality compared with others. With the framework of this paper, we conclude that 14-day quarantine period can largely interrupt the transmission of COVID-19, however, people who need specially monitoring should be isolated for about 20 days for the sake of safety. The results provide some suggestions for the prevention and control of COVID-19. The newly proposed ECIMM algorithm can also be used to deal with the doubly interval-censored data model appearing in various fields.
TL;DR: In this paper, a new (3 + 1)-dimensional Schrodinger equation in quantum mechanics is derived via compatibility condition via the compatibility condition, and conservation laws are obtained for soliton solutions.
Abstract: In the present paper, a new (3 + 1)-dimensional Schrodinger equation in Quantum Mechanics is derived. Based on the extended (3 + 1)-dimensional zero curvature equation, this equation is derived for the first time via the compatibility condition. Meanwhile, some soliton solutions are presented. Finally, conservation laws also obtained.
TL;DR: In this paper, a spur gear dynamic model is presented, where the detailed deformations of individual teeth are considered, including the tooth flexible deformations, gear body deformation, the local teeth contact deflections, and the tooth deformations due to its neighboring loaded tooth.
Abstract: Gear tooth profile deviations are usually inevitable due to the application of intentional tooth profile modification, the existence of undesired gear manufacturing errors and the tooth surface defects during operation, and they have been demonstrated to have significant effect on the vibration and noise level of gear transmissions. How to calculate the gear mesh forces accurately is crucial for gear dynamic simulation, especially in the presence of gear tooth profile deviations that will complicate the interactions at the gear mesh interface. This paper presents a spur gear dynamic model where the detailed deformations of individual teeth are considered, including the tooth flexible deformations, gear body deformations, the local teeth contact deflections, and the tooth deformations due to its neighboring loaded tooth. This dynamic model is validated by experimental test results with and without tooth tip reliefs. Then, the optimization of the tooth tip relief is performed. Finally, it is compared with three traditional dynamic models to reveal their discrepancies and applicability which could supply theoretical guidance for selection of gear dynamic models.
TL;DR: In this article, a review of nonlinear methods for model order reduction in structures with geometric nonlinearity is presented, with a special emphasis on the techniques based on invariant manifold theory.
Abstract: This paper aims at reviewing nonlinear methods for model order reduction in structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear-based techniques by their use of a nonlinear mapping instead of adding new vectors to enlarge the projection basis. Invariant manifolds have been first introduced in vibration theory within the context of nonlinear normal modes and have been initially computed from the modal basis, using either a graph representation or a normal form approach to compute mappings and reduced dynamics. These developments are first recalled following a historical perspective, where the main applications were first oriented toward structural models that can be expressed thanks to partial differential equations. They are then replaced in the more general context of the parametrisation of invariant manifold that allows unifying the approaches. Then, the specific case of structures discretised with the finite element method is addressed. Implicit condensation, giving rise to a projection onto a stress manifold, and modal derivatives, used in the framework of the quadratic manifold, are first reviewed. Finally, recent developments allowing direct computation of reduced-order models relying on invariant manifolds theory are detailed. Applicative examples are shown and the extension of the methods to deal with further complications are reviewed. Finally, open problems and future directions are highlighted.
TL;DR: Simulation experiments and security evaluations show that the algorithm can encrypt the color image effectively and has good security to resist various kinds of attacks.
Abstract: A novel color image encryption algorithm based on a cross 2D hyperchaotic map is proposed in this paper. The cross 2D hyperchaotic map is constructed using one nonlinear function and two chaotic maps with a cross structure. Chaotic behaviors are illustrated using bifurcation diagrams, Lyapunov exponent spectra, phase portraits, etc. In the color image encryption algorithm, the keys are generated using hash function SHA-512 and the information of the plain color image. First, the color plain image is converted to a combined bit-level matrix and permuted by the chaos-based row and column combined cycle shift scrambling method. Then, the scrambled integer matrix is diffused according to the selecting sequence which depends on the chaotic sequence. Last, decompose the diffusion matrix to get the encrypted color image. Simulation experiments and security evaluations show that the algorithm can encrypt the color image effectively and has good security to resist various kinds of attacks.
TL;DR: In this paper, a review of the nonlinear aspects of the mechanical inerter is presented, and the historical context goes back to the development of isolators and absorbers in the first half of the twentieth century.
Abstract: In this paper, a review of the nonlinear aspects of the mechanical inerter will be presented. The historical context goes back to the development of isolators and absorbers in the first half of the twentieth century. Both mechanical and fluid-based nonlinear inerter devices were developed in the mid- and late twentieth century. However, interest in the inerter really accelerated in the early 2000s following the work of Smith [87], who coined the term ‘inerter’ in the context of a force–current analogy between electrical and mechanical networks. Following the historical context, both fluid and mechanical inerter devices will be reviewed. Then, the application of nonlinear inerter-based isolators and absorbers is discussed. These include different types of nonlinear energy sinks, nonlinear inerter isolators and geometrically nonlinear inerter devices, many relying on concepts such as quasi-zero-stiffness springs. Finally, rocking structures with inerters attached are considered, before conclusions and some future directions for research are presented.
TL;DR: Through combining the adaptive method and tracking control method, where the target tracking trajectories are the estimate values from adaptive laws, the boundedness and stability of system states are guaranteed in this paper.
Abstract: This paper investigates the attack-resilient control problem for Markov jump systems (MJSs) with additive attacks. Both the sensor attacks and actuator attacks are taken into account in this paper, which make the attack-resilient control problem particularly complex. Moreover, different from multiplicative sensor attacks, the additive attacks are addressed in this paper. The adaptive laws based on projection operation are designed to ensure that the estimations of the unknown parameters are bounded. Based on the adaptive laws, the novel adaptive attack-resilient control strategy is proposed. Then, through combining the adaptive method and tracking control method, where the target tracking trajectories are the estimate values from adaptive laws, the boundedness and stability of system states are guaranteed in this paper. Finally, the adaptive attack-resilient control strategy is applied into an application example to illustrate the effectiveness.
TL;DR: In this paper, a variable-coefficient nonlinear Schrodinger equation that describes the optical soliton propagation in dispersion management fiber systems is studied, and two and three soliton solutions are obtained by using the Hirota bilinear method.
Abstract: In this paper, a variable-coefficient nonlinear Schrodinger equation that describes the optical soliton propagation in dispersion management fiber systems is studied. Two- and three-soliton solutions are obtained by using the Hirota bilinear method. Based on those solutions, the effects of related parameters on optical soliton propagation are discussed. By choosing different values of the third-order dispersion, the amplification of optical solitons can be realized. In addition, the interactions among the solitons can be reduced by setting a proper value of the group velocity dispersion. The results of this paper may be helpful to design optical amplifiers or to improve the quality of optical communications.
TL;DR: This paper considers a small-world network of photosensitive neurons and shows that the network exhibits synchronization in a specific range of coupling strengths before transcending into a chimera state.
Abstract: Recently, a photosensitive model has been proposed that takes into account nonlinear encoding and responses of photosensitive neurons that are subject to optical signals. In the model, a photocell term has been added to the well-known FitzHugh–Nagumo neuron, which results in a time-varying voltage source. The modified model exhibits most of the main characteristics of biological neurons, like spiking, bursting, and chaotic responses, but is also amenable to study the effect of optical signals. In this paper, we consider a small-world network of photosensitive neurons and study their collective behavior in dependence on interaction strength. We show that the network exhibits synchronization in a specific range of coupling strengths before transcending into a chimera state. We use the master stability function, a local-order parameter, as well as recurrence plots to verify the reported results.
TL;DR: The aim of this work is to provide a resource to the novice researcher in the field to facilitate the choice of the appropriate contact model for their work.
Abstract: In the present work, an introduction to the contact phenomena in multibody systems is made. The different existing approaches are described, together with their most distinctive features. Then, the term of coefficient of restitution is emphasized as a tool to characterize impact events and the algorithm for calculating the relative indentation between two convex-shaped bodies is developed. Subsequently, the main penalty contact models developed in the last decades are presented and developed, analysing their advantages and drawbacks, as well as their respective applications. Furthermore, some models with specific peculiarities that could be useful to the reader are included. The aim of this work is to provide a resource to the novice researcher in the field to facilitate the choice of the appropriate contact model for their work.