Showing papers in "Nonlinear Dynamics in 2020"

SEIR modeling of the COVID-19 and its dynamics.

Abstract: In this paper, a SEIR epidemic model for the COVID-19 is built according to some general control strategies, such as hospital, quarantine and external input Based on the data of Hubei province, the particle swarm optimization (PSO) algorithm is applied to estimate the parameters of the system We found that the parameters of the proposed SEIR model are different for different scenarios Then, the model is employed to show the evolution of the epidemic in Hubei province, which shows that it can be used to forecast COVID-19 epidemic situation Moreover, by introducing the seasonality and stochastic infection the parameters, nonlinear dynamics including chaos are found in the system Finally, we discussed the control strategies of the COVID-19 based on the structure and parameters of the proposed model

An image encryption scheme based on a new hybrid chaotic map and optimized substitution box

Abstract: This paper proposes a new hybrid chaotic map and a different way of using optimization technique to improve the performance of encryption algorithms. Compared to other chaotic functions, the proposed chaotic map establishes an excellent randomness performance and sensitivity. Based on its Lyapunov exponents and entropy measure, the characteristics of the new mathematical function are better than those of classical maps. We propose a new image cipher based on confusion/diffusion Shannon properties. The substitution phase of the proposed encryption algorithm, which depends on a new optimized substitution box, was carried out by chaotic Jaya optimization algorithm to generate S-boxes according to their nonlinearity score. The goal of the optimization process is to have a bijective matrix with high nonlinearity score. Furthermore, a dynamic key depending on the output of encrypted image is proposed. Security analysis indicates that the proposed encryption scheme can withstand different crypt analytics attacks.

Designs, analysis, and applications of nonlinear energy sinks

Abstract: Nonlinear energy sink (NES) is an appropriately designed nonlinear oscillator without positive linear stiffness. NES can suppress vibrations over a wide frequency range due to its targeted energy transfer characteristics. Thus, investigations on NES have attracted a lot of attention since a NES was proposed. Designs, analysis, and applications of NESs are still active since different configurations are needed in various practical circumstances. The present work provides a comprehensive review of state-of-the-art researches on NESs. The work begins with a survey of the generation of a NES and its important vibration control characteristics. The work highlights possible complex dynamics resulting in a NES coupled to a structure. The work also summarizes some significant design on the implements of optimal damping effects and the offsets of NES shortcomings. Then, the work details the applications of NESs in all engineering fields. The concluding remarks suggest further promising directions, such as NESs for multidirectional vibration reduction, NESs with nonlinearities beyond the cubic, potential deterioration caused by a NES, low-cost NESs, NESs for extremely low frequency range, and NESs integrated into active vibration controls. There are 383 references in the review, including some publications of the authors.

Generalized logistic growth modeling of the COVID-19 outbreak: comparing the dynamics in the 29 provinces in China and in the rest of the world.

Abstract: Started in Wuhan, China, the COVID-19 has been spreading all over the world We calibrate the logistic growth model, the generalized logistic growth model, the generalized Richards model and the generalized growth model to the reported number of infected cases for the whole of China, 29 provinces in China, and 33 countries and regions that have been or are undergoing major outbreaks We dissect the development of the epidemics in China and the impact of the drastic control measures both at the aggregate level and within each province We quantitatively document four phases of the outbreak in China with a detailed analysis on the heterogeneous situations across provinces The extreme containment measures implemented by China were very effective with some instructive variations across provinces Borrowing from the experience of China, we made scenario projections on the development of the outbreak in other countries We identified that outbreaks in 14 countries (mostly in western Europe) have ended, while resurgences of cases have been identified in several among them The modeling results clearly show longer after-peak trajectories in western countries, in contrast to most provinces in China where the after-peak trajectory is characterized by a much faster decay We identified three groups of countries in different level of outbreak progress, and provide informative implications for the current global pandemic

Firing multistability in a locally active memristive neuron model

Abstract: The theoretical, numerical and experimental demonstrations of firing dynamics in isolated neuron are of great significance for the understanding of neural function in human brain. In this paper, a new type of locally active and non-volatile memristor with three stable pinched hysteresis loops is presented. Then, a novel locally active memristive neuron model is established by using the locally active memristor as a connecting autapse, and both firing patterns and multistability in this neuronal system are investigated. We have confirmed that, on the one hand, the constructed neuron can generate multiple firing patterns like periodic bursting, periodic spiking, chaotic bursting, chaotic spiking, stochastic bursting, transient chaotic bursting and transient stochastic bursting. On the other hand, the phenomenon of firing multistability with coexisting four kinds of firing patterns can be observed via changing its initial states. It is worth noting that the proposed neuron exhibits such firing multistability previously unobserved in single neuron model. Finally, an electric neuron is designed and implemented, which is extremely useful for the practical scientific and engineering applications. The results captured from neuron hardware experiments match well with the theoretical and numerical simulation results.

Hidden extreme multistability with hyperchaos and transient chaos in a Hopfield neural network affected by electromagnetic radiation

Abstract: Biological nervous system function is closely related to its dynamical behaviors, and some dynamical phenomena observed in biological systems can be detected in the simplified neural models. In this paper, the chaotic dynamics in a three-neuron-based Hopfield neural network (HNN) with stimulation of electromagnetic radiation is investigated. The neural network is modeled by utilizing a flux-controlled memristor to describe the effects of electromagnetic field on neurons. The simple neural model affected by electromagnetic radiation does not contain any equilibrium points, but can induce coexisting infinitely many hidden attractors, such as hyperchaos, transient hyperchaos, period, quasi-period, chaos as well as transient chaos with different chaotic times. In particular, the dynamics of hidden extreme multistability with hyperchaos and transient chaos in the neural network highly depends on the system parameters and state initial values. The coexistence of multiple hidden attractors is revealed via applying a host of numerical analysis methods including phase plots, time sequence waveforms, bifurcation diagrams, Lyapunov exponents and attraction basins. Besides, a HNN-based circuit consisting of commercially available electronic elements is designed to verify the theoretical analysis. Hardware measurement and MULTISIM simulation results are basically consistent with MATLAB numerical simulation results.

Dromion-like structures and periodic wave solutions for variable-coefficients complex cubic–quintic Ginzburg–Landau equation influenced by higher-order effects and nonlinear gain

Abstract: In this work, the variable-coefficients complex cubic–quintic Ginzburg–Landau equation (CCQGLE) influenced by higher-order effects and nonlinear gain is considered. Based on the asymmetric method, analytic one-soliton solution for the variable-coefficients CCQGLE is constructed for the first time. In addition, with some certain conditions, the periodic wave and dromion-like structures are derived. The results obtained may be helpful in understanding the solitons amplification and solitons management in optical fiber.

A novel simple chaotic circuit based on memristor–memcapacitor

Abstract: In this paper, we focus on a novel simple chaotic circuit with a memristor, a memcapacitor and a linear inductor in parallel. Then we establish the circuit’s dimensionless mathematical model. Nineteen types of different chaotic attractors are found in the circuit. The chaotic system’s equilibrium point and stability are analyzed by using the traditional dynamic analysis methods, and the dynamical behaviors with three varying parameters of this circuit are analyzed in detail. Furthermore, some special phenomena such as state transition, chaos degradation and the multiple coexisting attractors are discovered. Finally, we implement this circuit through the DSP platform and the results illustrate the validity of the theoretical analysis. Theoretical analysis and simulation results indicate that the simple chaotic circuit has very rich dynamical characteristics.

A fractional-order model for the novel coronavirus (COVID-19) outbreak.

Abstract: The outbreak of the novel coronavirus (COVID-19), which was firstly reported in China, has affected many countries worldwide To understand and predict the transmission dynamics of this disease, mathematical models can be very effective It has been shown that the fractional order is related to the memory effects, which seems to be more effective for modeling the epidemic diseases Motivated by this, in this paper, we propose fractional-order susceptible individuals, asymptomatic infected, symptomatic infected, recovered, and deceased (SEIRD) model for the spread of COVID-19 We consider both classical and fractional-order models and estimate the parameters by using the real data of Italy, reported by the World Health Organization The results show that the fractional-order model has less root-mean-square error than the classical one Finally, the prediction ability of both of the integer- and fractional-order models is evaluated by using a test data set The results show that the fractional model provides a closer forecast to the real data

Coupled spatial periodic waves and solitons in the photovoltaic photorefractive crystals

Abstract: The evolution of spatial solitons in the photovoltaic photorefractive crystal can be governed by the specific coupled nonlinear Schrodinger equations. Under the photovoltaic field with the external bias field, the coupled cn–sn-type periodic wave solution and the corresponding photorefractive bright–dark soliton pair were constructed to describe the evolution of beam. The influence of the external bias field on solitonic dynamics is analyzed. In the photovoltaic crystal, coupled sn–cn-type, sn–dn-type periodic wave solutions, solution constructed by products of elliptic functions and the corresponding dark–bright soliton pair and coupled double-peaked soliton solutions are found to describe the evolution of a spatial-phase-modulated photovoltaic soliton and a non-phase-modulated beam.

Transmission dynamics of COVID-19 in Wuhan, China: effects of lockdown and medical resources.

Abstract: Due to the strong infectivity of COVID-19, it spread all over the world in about three months and thus has been studied from different aspects including its source of infection, pathological characteristics, diagnostic technology and treatment Yet, the influences of control strategies on the transmission dynamics of COVID-19 are far from being well understood In order to reveal the mechanisms of disease spread, we present dynamical models to show the propagation of COVID-19 in Wuhan Based on mathematical analysis and data analysis, we systematically explore the effects of lockdown and medical resources on the COVID-19 transmission in Wuhan It is found that the later lockdown is adopted by Wuhan, the fewer people will be infected in Wuhan, and nevertheless it will have an impact on other cities in China and even the world Moreover, the richer the medical resources, the higher the peak of new infection, but the smaller the final scale These findings well indicate that the control measures taken by the Chinese government are correct and timely

Robust fixed-time attitude stabilization control of flexible spacecraft with actuator uncertainty

Abstract: A robust fixed-time control framework is presented to stabilize flexible spacecraft’s attitude system with external disturbance, uncertain parameters of inertia, and actuator uncertainty. As a stepping stone, a nonlinear system having faster fixed-time convergence property is preliminarily proposed by introducing a time-varying gain into the conventional fixed-time stability method. This gain improves the convergence rate. Then, a fixed-time observer is proposed to estimate the uncertain torque induced by disturbance, uncertain parameters of inertia, and actuator uncertainty. Fixed-time stability is ensured for the estimation error. Using this estimated knowledge and the full-states’ measurements, a nonsingular terminal sliding controller is finally synthesized. This is achieved via a nonsingular and faster terminal sliding surface with faster convergence rate. The closed-loop attitude stabilization system is proved to be fixed-time stable with the convergence time independent of initial states. The attitude stabilization performance is robust to disturbance and uncertainties in inertia and actuators. Simulation results are also shown to validate the attitude stabilization performance of this control approach.

Memristor synapse-coupled memristive neuron network: synchronization transition and occurrence of chimera

Abstract: Memristor synapse can be used to characterize the electromagnetic induction effect between two neurons that induces an action current by their membrane potential difference. This paper proposes a memristor synapse-coupled neuron network with no equilibrium, which is achieved using a memristor synapse to connect the membrane potentials of two identical three-dimensional memristive Hindmarsh–Rose neurons. Exponential synchronization is proved theoretically, and synchronous activities are discussed numerically. The theoretical and numerical results illustrate that the synchronicities of memristor synapse-coupled neuron network are related to the memristor coupling coefficient and especially related to the initial states of memristor synapse and coupling neurons. Furthermore, by constructing a ring network of memristor synapse-coupled neuron network, several types of collective behaviors including incoherent, coherent, imperfect synchronization, and chimera states are disclosed numerically, which indicate that the chimera states arisen in the ring network are dependent on the memristor coupling coefficient and sub-network coupling strength.

Initial offset boosting coexisting attractors in memristive multi-double-scroll Hopfield neural network

Abstract: Memristors are widely considered to be promising candidates to mimic biological synapses. In this paper, by introducing a non-ideal flux-controlled memristor model into a Hopfield neural network (HNN), a novel memristive HNN model with multi-double-scroll attractors is constructed. The parity of the number of double scrolls can be flexibly controlled by the internal parameters of the memristor. Through theoretical analysis and numerical simulation, various coexisting attractors and amplitude control are observed. Particularly, the interesting and rare phenomenon of the memristor initial offset boosting coexisting dynamics is discovered, in which the initial offset boosting coexisting double-scroll attractors with banded attraction basins are distributed in a line along the boosting route with the variation of the memristor initial condition. In addition, it is also found that the number of the initial offset boosting coexisting double-scroll attractors is closely related to the total number of scrolls and ultimately tends to infinity with increasing the total number of scrolls, meaning the emergence of extreme multistability. Then, the random performance of the initial offset boosting coexisting double-scroll attractors is tested by the NIST test suite. Moreover, an encryption scheme based on them is also proposed. The obtained results show that they have excellent randomness and are suitable for image encryption application. Finally, numerical simulation results are well demonstrated by circuit experiments, showing the feasibility of the designed memristive multi-double-scroll HNN model.

A new discrete-space chaotic map based on the multiplication of integer numbers and its application in S-box design

Abstract: In this paper, a new one-dimensional discrete-space chaotic map based on the multiplication of integer numbers and circular shift is presented. Dynamical properties of the proposed map are analyzed, and it exhibits chaotic behavior. The proposed map has fixed points for certain settings, but it is easy to completely avoid them. This map preserves all desirable properties of previous discrete-space chaotic maps and has improved characteristics related to orbit length, computational complexity and memory requirements. These improvements can be particularly useful when implementation in digital devices, which have limited memory and computational resources, is needed. S-box design method based on this chaotic map is presented as an example of its application in cryptography. The results of performance tests show that S-boxes with good cryptographic properties can be generated on the basis of this discrete-space chaotic map.

Robust identification for fault detection in the presence of non-Gaussian noises: application to hydraulic servo drives

Abstract: Intensive research in the field of mathematical modeling of hydraulic servo systems has shown that their mathematical models have many important details which cannot be included in the model. Due to impossibility of direct measurement or calculation of dimensions of certain components, leakage coefficients or friction coefficients, it was supposed that parameters of the hydraulic servo system are random. On the other side, it has been well known that the hydraulic servo system can be approximated by a linear model with time-varying parameters. An estimation of states and time-varying parameters of linear state-space models is of practical importance for fault diagnosis and fault-tolerant control. Previous works on this topic consider estimation in Gaussian noise environment, but not in the presence of outliers. The known fact is that the measurements have inconsistent observations with the largest part of the observation population (outliers). They can significantly make worse the properties of linearly recursive algorithms which are designed to work in the presence of Gaussian noises. This paper proposes the strategy of parameter–state robust estimation of linear state-space models in the presence of all possible faults and non-Gaussian noises. Because of its good features in robust filtering, Masreliez–Martin filter represents a cornerstone for realization of the robust algorithm. The good features of the proposed robust algorithm to identification of the hydraulic servo system are illustrated by intensive simulations.

A hidden mode observation approach to finite-time SOFC of Markovian switching systems with quantization

Abstract: This paper investigates the finite-time static output feedback control of Markovian switching systems, where quantization effects are taken into consideration from plant to controller and controller to actuator, simultaneously. The resulting system is more general, where asynchronous control, quantization, actuator failure, and external disturbance are covered. Furthermore, a descriptor representation method is employed to eliminate both the coupling term and the quantization effects. Owing to a hidden mode observation approach, sufficient conditions are achieved to guarantee the finite-time stochastic boundedness of the resulting system, and the finite-time output feedback controller is designed. Finally, a vehicle’s throttle actuator is exploited to confirm the feasibility of the proposed method.

Managements of scalar and vector rogue waves in a partially nonlocal nonlinear medium with linear and harmonic potentials

Abstract: We consider a ( $$2+1$$ )-dimensional nonautonomous-coupled nonlinear Schrodinger equation, which includes the partially nonlocal nonlinearity under linear and harmonic potentials. Via a projecting expression between nonautonomous and autonomous equations, and utilizing the bilinear method and Darboux transformation method, we find diversified exact solutions. These solutions contain the nonlocal rogue wave and Akhmediev or Ma breather solutions, and the combined solution which describes a rogue wave superposed on an Akhmediev or Ma breather. By adjusting values of diffraction, width and phase chirp parameters of wave, the maximum value of the accumulated time can be modulated. When we compare the maximum value of the accumulated time with that of the excitation position parameters, we study the management of scalar and vector rogue waves, such as the excitations of full shape, early shape and climax shape for rogue waves.

A review on computational intelligence for identification of nonlinear dynamical systems

Abstract: This work aims to provide a broad overview of computational techniques belonging to the area of artificial intelligence tailored for identification of nonlinear dynamical systems. Both parametric and nonparametric identification problems are considered. The examined computational intelligence techniques for parametric identification deal with genetic algorithm, particle swarm optimization, and differential evolution. Special attention is paid to the parameters estimation for a rich class of nonlinear dynamical models, including the Bouc–Wen model, chaotic systems, the Jiles–Atherton model, the LuGre model, the Prandtl–Ishlinskii model, the Preisach model, and the Wiener–Hammerstein model. On the other hand, genetic programming and artificial neural networks are discussed for nonparametric identification applications. Once the identification problem is formulated, a detailed illustration of the considered computational intelligence techniques is provided, together with a comprehensive examination of relevant applications in the fields of structural mechanics and engineering. Possible directions for future research are also addressed.

Solitons and periodic waves for the (2 + 1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics

Abstract: Fluid mechanics has the applications in a wide range of disciplines, such as oceanography, astrophysics, meteorology, and biomedical engineering. Under investigation in this paper is the ($$2+1$$)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics. Via the Pfaffian technique and certain constraint on the real constant $$\alpha $$, the Nth-order Pfaffian solutions are derived. One- and two-soliton solutions are obtained via the Nth-order Pfaffian solutions. Based on the Hirota–Riemann method, one- and two-periodic wave solutions are constructed. With the help of the analytic and graphic analysis, we notice that: (1) of the one soliton, amplitude is irrelevant to $$\gamma $$, a real constant coefficient in the equation, velocity along the x direction is independent of $$\gamma $$, while velocity along the y direction is proportional to $$\gamma $$; (2) one soliton keeps its amplitude and velocity invariant during the propagation and total amplitude of the two solitons in the interaction region is lower than that of any soliton; (3) one-periodic wave can be viewed as a superposition of the overlapping solitary waves, placed one period apart; (4) periodic behaviors for the two-periodic wave exist along the x and y directions, respectively; (5) under certain limiting conditions, one-periodic wave solutions approach to the one-soliton solutions and two-periodic wave solutions approach to the two-soliton solutions.

Bilinear form, soliton, breather, lump and hybrid solutions for a ( $$\varvec{2+1}$$ 2 + 1 )-dimensional Sawada–Kotera equation

Abstract: In this paper, we investigate a ( $$2+1$$ )-dimensional Sawada–Kotera (SK) equation for the atmosphere, rivers, lakes, oceans, as well as the conformal field and two-dimensional quantum gravity gauge field. Bilinear form and N-soliton solutions, which are different from those in the existing literatures, are derived, where N is a positive integer. The higher-order breather, lump and hybrid solutions for the ( $$2+1$$ )-dimensional SK equation are also constructed based on the N-soliton solutions. Three kinds of the first-order breathers are obtained, and the higher-order breathers are constructed. The higher-order lump solutions are also derived via the long-wave limit method. Hybrid solutions composed of the solitons, breathers and lumps are worked out, and interaction between the waves is discussed graphically. Finally, similar solutions for a generalized form of the ( $$2+1$$ )-dimensional SK equation are given.

Observer-based adaptive neural tracking control for output-constrained switched MIMO nonstrict-feedback nonlinear systems with unknown dead zone

Abstract: In this paper, the issue of adaptive neural tracking control for uncertain switched multi-input multi-output (MIMO) nonstrict-feedback nonlinear systems with average dwell time is studied. The system under consideration includes unknown dead-zone inputs and output constraints. The uncertain nonlinear functions are identified via neural networks. Also, neural networks-based switched observer is constructed to approximate all unmeasurable states. By means of the information for dead-zone slopes and barrier Lyapunov function (BLF), the problems of dead-zone inputs and output constraints are tackled. Furthermore, dynamic surface control (DSC) scheme is employed to ensure that the computation burden is greatly reduced. Then, an observer-based adaptive neural control strategy is developed on the basis of backstepping technique and multiple Lyapunov functions approach. Under the designed controller, all the signals existing in switched closed-loop system are bounded, and system outputs can track the target trajectories within small bounded errors. Finally, the feasibility of the presented control algorithm is proved via simulation results.

Global dynamics of a multi-strain SEIR epidemic model with general incidence rates: application to COVID-19 pandemic.

Abstract: This paper investigates the global stability analysis of two-strain epidemic model with two general incidence rates. The problem is modelled by a system of six nonlinear ordinary differential equations describing the evolution of susceptible, exposed, infected and removed individuals. The wellposedness of the suggested model is established in terms of existence, positivity and boundedness of solutions. Four equilibrium points are given, namely the disease-free equilibrium, the endemic equilibrium with respect to strain 1, the endemic equilibrium with respect to strain 2, and the last endemic equilibrium with respect to both strains. By constructing suitable Lyapunov functional, the global stability of the disease-free equilibrium is proved depending on the basic reproduction number $$R_0$$ . Furthermore, using other appropriate Lyapunov functionals, the global stability results of the endemic equilibria are established depending on the strain 1 reproduction number $$R^{1}_0$$ and the strain 2 reproduction number $$R^{2}_0$$ . Numerical simulations are performed in order to confirm the different theoretical results. It was observed that the model with a generalized incidence functions encompasses a large number of models with classical incidence functions and it gives a significant wide view about the equilibria stability. Numerical comparison between the model results and COVID-19 clinical data was conducted. Good fit of the model to the real clinical data was remarked. The impact of the quarantine strategy on controlling the infection spread is discussed. The generalization of the problem to a more complex compartmental model is illustrated at the end of this paper.

Short memory fractional differential equations for new memristor and neural network design

Abstract: Fractional derivatives hold memory effects, and they are extensively used in various real-world applications. However, they also need large storage space and cause poor efficiency. In this paper, some standard definitions are revisited. Then, short memory fractional derivatives and a short memory fractional modeling approach are introduced. Numerical solutions are given by the use of the predictor–corrector method. The short memory is adopted for fractional modeling of memristor, neural networks and materials’ relaxation property. Global stability conditions of variable-order neural networks are derived. The new features of short memory fractional differential equations are used to improve the performance of networks. The results are illustrated in comparison with standard ones. Finally, discussions are made about potential applications.

Forecast analysis of the epidemics trend of COVID-19 in the USA by a generalized fractional-order SEIR model.

Abstract: In this paper, a generalized fractional-order SEIR model is proposed, denoted by SEIQRP model, which divided the population into susceptible, exposed, infectious, quarantined, recovered and insusceptible individuals and has a basic guiding significance for the prediction of the possible outbreak of infectious diseases like the coronavirus disease in 2019 (COVID-19) and other insect diseases in the future. Firstly, some qualitative properties of the model are analyzed. The basic reproduction number R0 is derived. When R0 1 , the endemic equilibrium point is also unique. Furthermore, some conditions are established to ensure the local asymptotic stability of disease-free and endemic equilibrium points. The trend of COVID-19 spread in the USA is predicted. Considering the influence of the individual behavior and government mitigation measurement, a modified SEIQRP model is proposed, defined as SEIQRPD model, which is divided the population into susceptible, exposed, infectious, quarantined, recovered, insusceptible and dead individuals. According to the real data of the USA, it is found that our improved model has a better prediction ability for the epidemic trend in the next two weeks. Hence, the epidemic trend of the USA in the next two weeks is investigated, and the peak of isolated cases is predicted. The modified SEIQRP model successfully capture the development process of COVID-19, which provides an important reference for understanding the trend of the outbreak.

Controlling effect of vector and scalar crossed double-Ma breathers in a partially nonlocal nonlinear medium with a linear potential

Abstract: We follow our interest in a nonautonomous (2+1)-dimensional coupled nonlinear Schrodinger equation with partially nonlocal nonlinear effect and a linear potential, and get a relational expression mapping nonautonomous equation into autonomous one. Further applying the Darboux method, we find affluent vector and scalar solutions, including the crossed double-Ma breather solution. Regulating values of initial width, initial chirp and diffraction parameters so that the maximal value of accumulated time changes to compare with values of peak positions, we actualize the controlling effect of vector and scalar crossed double-Ma breathers including the complete shape, crest shape and nascent shape excitations in different linear potentials.

Rare and extreme events: the case of COVID-19 pandemic.

Abstract: Complex systems have characteristics that give rise to the emergence of rare and extreme events. This paper addresses an example of such type of crisis, namely the spread of the new Coronavirus disease 2019 (COVID-19). The study deals with the statistical comparison and visualization of country-based real-data for the period December 31, 2019, up to April 12, 2020, and does not intend to address the medical treatment of the disease. Two distinct approaches are considered, the description of the number of infected people across time by means of heuristic models fitting the real-world data, and the comparison of countries based on hierarchical clustering and multidimensional scaling. The computational and mathematical modeling lead to the emergence of patterns, highlighting similarities and differences between the countries, pointing toward the main characteristics of the complex dynamics.

Adaptive integral sliding mode control with payload sway reduction for 4-DOF tower crane systems

Abstract: An adaptive integral sliding mode control (AISMC) method with payload sway reduction is presented for 4-DOF tower cranes in this paper. The designed controller consists of three parts: The integral sliding mode control is used to provide the robust behavior; the adaptive control is utilized to present the adaptive performance; the swing-damping term is added to suppress and eliminate the payload swing angles. Different from existing sliding mode control methods presenting with chattering phenomenon, the proposed AISMC method is essentially continuous and chattering free. Moreover, the accurate values of the system parameters including the payload mass, the trolley mass, the cable length, the moment of inertia of the jib, the friction-related coefficients are not required for the designed controller due to the adaptive control. Lyapunov-based analysis and LaSalle’s invariance principle are employed to support the theoretical derivations without linearizing the nonlinear dynamics. Experimental results are illustrated to show the superior control performance of the designed controller.

A robust image encryption scheme using chaotic tent map and cellular automata

Abstract: This paper suggests a unique image encryption scheme based on key-based block ciphering followed by shuffling of ciphered bytes with variable-sized blocks, which makes this scheme substantially robust compared to other contemporary schemes available. Another distinguishing feature of this scheme is the usage of variable-sized key streams for consecutive blocks. Based on the elementary cellular automata with chaotic tent map, distinct key streams are used to cipher individual blocks. In the subsequent step, the bytes of the ciphered block so obtained are further shuffled to make the scheme more diffused. The block size varies with the varying key stream, which is again dependent on the preceding key stream as well as the plain image. It needs to be mentioned that the size of the first block and the key stream are generated from a 64-byte secret key and the plain image. Values of correlation and the number of pixel change rate between the original and the encrypted images are 0.000479 and 99.620901, respectively. Both of the above results along with other relevant experimental results strongly establish the robustness of the proposed scheme.

Colour light field image encryption based on DNA sequences and chaotic systems

Abstract: The light field image (LFI) information includes the intensity of the collected object and the direction of the light through recording. An LFI with a 4-D scene representation includes a 2-D spatial domain and a 2-D angular domain, which is completely different than general natural images. To date, the encryption of natural images has been widely studied, while the encryption design of the LFI is missing. This work proposes an encryption scheme for colour LFI based on DNA sequences and chaotic systems. First, we employ an angular domain plane to represent the multi-view image of the LFI and then obtain a sub-view image in the spatial domain. For the given sub-view image and the random matrix, we apply a block processing method to divide multiple sub-blocks. Then, the DNA sequence and the chaotic system are used to encrypt the sub-view image. Moreover, considering the relationship between two planes, we apply the Arnold transform for all the sub-view images to realize the final encryption. Through three statistical analyses, three resistance attack analyses and two key analyses, experimental results show that the proposed scheme can be applicable, reliable, and secure enough.