Showing papers in "Nonlinear Dynamics in 2017"

An image encryption scheme based on chaotic tent map

Abstract: Image encryption has been an attractive research field in recent years. The chaos-based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques. This paper proposes a novel image encryption scheme, which is based on the chaotic tent map. Image encryption systems based on such map show some better performances. Firstly, the chaotic tent map is modified to generate chaotic key stream that is more suitable for image encryption. Secondly, the chaos-based key stream is generated by a 1-D chaotic tent map, which has a better performance in terms of randomness properties and security level. The performance and security analysis of the proposed image encryption scheme is performed using well-known ways. The results of the fail-safe analysis are inspiring, and it can be concluded that the proposed scheme is efficient and secure.

A review for dynamics in neuron and neuronal network

Abstract: The biological Hodgkin–Huxley model and its simplified versions have confirmed its effectiveness for recognizing and understanding the electrical activities in neurons, and bifurcation analysis is often used to detect the mode transition in neuronal activities. Within the collective behaviors of neurons, neuronal network with different topology is designed to study the synchronization behavior and spatial pattern formation. In this review, the authors give careful comments for the presented neuron models and present some open problems in this field, nonlinear analysis could be effective to further discuss these problems and some results could be helpful to give possible guidance in the field of neurodynamics.

Two-memristor-based Chua’s hyperchaotic circuit with plane equilibrium and its extreme multistability

Abstract: This paper presents a novel fifth-order two-memristor-based Chua’s hyperchaotic circuit, which is synthesized from an active band pass filter-based Chua’s circuit through replacing a nonlinear resistor and a linear resistor with two different memristors. This physical circuit has a plane equilibrium and therefore emerges complex phenomenon of extreme multistability. Based on the mathematical model, stability distributions of three nonzero eigenvalues in the equilibrium plane are exhibited, from which it is observed that four different stability regions with unstable saddle-focus, and stable and unstable node-focus are distributed, thereby leading to coexisting phenomenon of infinitely many attractors. Furthermore, extreme multistability depending on two-memristor initial conditions is investigated by bifurcation diagrams and Lyapunov exponent spectra and coexisting infinitely many attractors’ behavior is revealed by phase portraits and attraction basins. At last, a hardware circuit is fabricated and some experimental observations are captured to verify that extreme multistability indeed exists in the two-memristor-based Chua’s hyperchaotic circuit.

Recent advances in vibration control of offshore platforms

Abstract: Offshore platforms are widely used to explore, drill, produce, storage, and transport ocean resources and are usually subject to environmental loading, such as waves, winds, ice, and currents, which may lead to failure of deck facilities, fatigue failure of platforms, inefficiency of operation, and even discomfort of crews. In order to ensure reliability and safety of offshore platforms, it is of great significance to explore a proper way of suppressing vibration of offshore platforms. There are mainly three types of control schemes, i.e., passive control schemes, semi-active control schemes, and active control schemes, to deal with vibration of offshore platforms. This paper provides an overview of these schemes. Firstly, passive control schemes and several semi-active control schemes are briefly summarized. Secondly, some classical active control approaches, such as optimal control, robust control, and intelligent control, are briefly reviewed. Thirdly, recent advances of active control schemes with delayed feedback control, sliding model control, sampled-data control, and network-based control are deeply analyzed. Finally, some challenging issues are provided to guide future research directions.

Nonlinear transient isogeometric analysis of smart piezoelectric functionally graded material plates based on generalized shear deformation theory under thermo-electro-mechanical loads

Abstract: We present a generalized shear deformation theory in combination with isogeometric (IGA) approach for nonlinear transient analysis of smart piezoelectric functionally graded material (FGM) plates. The nonlinear transient formulation for plates is formed in the total Lagrange approach based on the von Karman strains, which includes thermo-piezoelectric effects, and solved by Newmark time integration scheme. The electric potential through the thickness of each piezoelectric layer is assumed to be linear. The material properties vary through the thickness of FGM according to the rule of mixture and the Mori–Tanaka schemes. Various numerical examples are presented to demonstrate the effectiveness of the proposed method.

Efficient cryptosystem approaches: S-boxes and permutation–substitution-based encryption

Abstract: In this paper, two efficient cryptosystem schemes in the form of permutation–substitution based on chaotic systems are proposed. Firstly, a simple and efficient S-box method is introduced in order to use this S-box designed scheme in secure color image encryption technique. The major advantage of the proposed strategy is the dynamic aspect of keys used by chaotic map to generate strong S-boxes. Secondly, an efficient color encryption scheme based on chaotic maps and S-boxes in the form of permutation–substitution network is developed. Experimental results show the effectiveness of the proposed schemes. The suggested cryptosystems have superior performance and great potential for prominent prevalence in cryptographic applications compared to previous schemes.

Coexistence of hidden chaotic attractors in a novel no-equilibrium system

Abstract: Hidden attractors have received considerable interest in physics, mechanics and other dynamical areas recently. This paper introduces a novel autonomous system with hidden attractor. In particular, there exists no-equilibrium point in this system. Although the new system is simple with six terms, it exhibits complex behavior such as chaos and multistability. In addition, the offset boosting of a variable is achieved by adding a single controlled constant. Dynamical properties of the no-equilibrium system have been discovered by using nonlinear dynamical tools as well as an electronic implementation.

Bäcklund transformation, multiple wave solutions and lump solutions to a (3 + 1)-dimensional nonlinear evolution equation

Abstract: In this paper, a $$(3+1)$$ -dimensional nonlinear evolution equation is cast into Hirota bilinear form with a dependent variable transformation. A bilinear Backlund transformation is then presented, which consists of six bilinear equations and involves nine arbitrary parameters. With multiple exponential function method and symbolic computation, nonresonant-typed one-, two-, and three-wave solutions are obtained. Furthermore, two classes of lump solutions to the dimensionally reduced cases with $$y=x$$ and $$y=z$$ are both derived. Finally, some figures are given to reveal the propagation of multiple wave solutions and lump solutions.

Solving the $$\mathbf{(3+1) }$$ ( 3 + 1 ) -dimensional KP–Boussinesq and BKP–Boussinesq equations by the simplified Hirota’s method

Abstract: We study two (3 $$+$$ 1)-dimensional generalized equations, namely the Kadomtsev–Petviashvili–Boussinesq equation and the B-type Kadomtsev–Petviashvili–Boussinesq equation. We use the simplified Hirota’s method to conduct this study and to find the general phase shift of these equations. We obtain one- and two-soliton solutions, for each equation, with the coefficients of the three spatial variables are left as free parameters. However, we also develop special conditions on the coefficients of the spatial variables guarantee the existence of three-soliton solutions for each of these two equation.

Antimonotonicity, chaos and multiple attractors in a novel autonomous memristor-based jerk circuit

Abstract: A novel memristor-based oscillator derived from the autonomous jerk circuit (Sprott in IEEE Trans Circuits Syst II Express Briefs 58:240–243, 2011) is proposed. A first-order memristive diode bridge replaces the semiconductor diode of the original circuit. The complex behavior of the oscillator is investigated in terms of equilibria and stability, phase space trajectories plots, bifurcation diagrams, graphs of Lyapunov exponents, as well as frequency spectra. Antimonotonicity (i.e. concurrent creation and destruction of periodic orbits), chaos, periodic windows and crises are reported. More interestingly, one of the main features of the novel memristive jerk circuit is the presence of a region in the parameters’ space in which the model develops hysteretic behavior. This later phenomenon is marked by the coexistence of four different (periodic and chaotic) attractors for the same values of system parameters, depending solely on the choice of initial conditions. Basins of attractions of various competing attractors display complex basin boundaries thus suggesting possible jumps between coexisting solutions in experiment. Compared to previously published jerk circuits with similar behavior, the novel system distinguishes by the presence of a single equilibrium point and a relatively simpler structure (only off-the-shelf electronic components are involved). Results of theoretical analyses are perfectly traced by laboratory experimental measurements.

A novel pseudorandom number generator based on pseudorandomly enhanced logistic map

Abstract: In last years, low-dimensional and high-dimensional chaotic systems have been implemented in cryptography. The efficiency and performance of these nonlinear systems play an important role in limited hardware implementations. In this context, low-dimensional chaotic systems are more attractive than high-dimensional chaotic systems to produce the pseudorandom key stream used for encryption purposes. Although low-dimensional chaotic maps present some security disadvantages when they are used in cryptography, they are highly attractive due its simple structure, discrete nature, less arithmetic operations, high output processing, and relatively easy to implement in a digital system. In this paper, we proposed both a pseudorandomly enhanced logistic map (PELM) and its application in a novel pseudorandom number generator (PRNG) algorithm, which produces pseudorandom stream with excellent statistical properties. The proposed PELM is compared with logistic map by using histograms and Lyapunov exponents to show its higher benefits in pseudorandom number generator. In contrast to recent schemes in the literature, we present a comprehensive security analysis over the proposed pseudorandom number generator based on pseudorandomly enhanced logistic map (PRNG–PELM) from a cryptographic point of view to show its potential use in secure communications. In addition, the randomness of the PRNG–PELM is verified with the most complete random test suit of National Institute of Standards and Technology (NIST 800-22) and with TestU01. Based on security results, few arithmetic operations required, and high output rate, the proposed PRNG–PELM scheme can be implemented in secure encryption applications, even in embedded systems with limited hardware resources.

Active disturbance rejection adaptive control of uncertain nonlinear systems: theory and application

Abstract: This paper proposes an active disturbance rejection adaptive controller for tracking control of a class of uncertain nonlinear systems with consideration of both parametric uncertainties and uncertain nonlinearities by effectively integrating adaptive control with extended state observer via backstepping method. Parametric uncertainties are handled by the synthesized adaptive law and the remaining uncertainties are estimated by extended state observer and then compensated in a feedforward way. Moreover, both matched uncertainties and unmatched uncertainties can be estimated by constructing an extended state observer for each channel of the considered nonlinear plant. Since parametric uncertainties can be reduced by parameter adaptation, the learning burden of extended state observer is much reduced. Consequently, high-gain feedback is avoided and improved tracking performance can be expected. The proposed controller theoretically guarantees a prescribed transient tracking performance and final tracking accuracy in general while achieving asymptotic tracking when the uncertain nonlinearities are not time-variant. The motion control of a motor-driven robot manipulator is investigated as an application example with some suitable modifications and improvements, and comparative simulation results are obtained to verify the high tracking performance nature of the proposed control strategy.

Nonlinear disturbance observer-based backstepping finite-time sliding mode tracking control of underwater vehicles with system uncertainties and external disturbances

Abstract: In this paper, a nonlinear disturbance observer-based backstepping finite-time sliding mode control scheme for trajectory tracking of underwater vehicles subject to unknown system uncertainties and time-varying external disturbances is proposed. To reduce the influence of the uncertainties and external disturbances, a nonlinear disturbance observer is developed without any acceleration measurements to identify the lumped disturbance term. Additionally, the finite-time trajectory tracking controller is designed by combining second-order sliding mode control and backstepping design technique with the nonlinear disturbance observer. The finite-time convergence of motion tracking errors and the stability of the overall closed-loop control system are guaranteed by the Lyapunov approach. Besides, comprehensive simulation studies on trajectory tracking control of underwater vehicles are provided to demonstrate the effectiveness and performance of the proposed control scheme.

FPGA implementation of novel fractional-order chaotic systems with two equilibriums and no equilibrium and its adaptive sliding mode synchronization

Abstract: This paper introduces two novel fractional-order chaotic systems with cubic nonlinear resistor and investigates its adaptive sliding mode synchronization. Firstly the novel two equilibrium chaotic system with cubic nonlinear resistor (NCCNR) is derived and its dynamic properties are investigated. The fractional-order cubic nonlinear resistor system (FONCCNR) is then derived from the integer-order model and its stability and fractional-order bifurcation are discussed. Next a novel no-equilibrium chaotic cubic nonlinear resistor system (NECNR) is derived from NCCNR system. Dynamic properties of NECNR system are investigated. The fractional-order no equilibrium cubic nonlinear resistor system (FONECNR) is derived from NECNR. Stability and fractional-order bifurcation are investigated for the FONECNR system. The non-identical adaptive sliding mode synchronization of FONCCNR and FONECNR systems are achieved. Finally the proposed systems, adaptive control laws, sliding surfaces and adaptive controllers are implemented in FPGA.

Lump solutions to the (\(\mathbf 2+1 \))-dimensional Sawada–Kotera equation

Abstract: In this paper, via generalized bilinear forms, we consider the ( $$2+1$$ )-dimensional bilinear p-Sawada–Kotera (SK) equation. We derive analytical rational solutions in terms of positive quadratic functions. Through applying the dependent transformation, we present a class of lump solutions of the ( $$2+1$$ )-dimensional SK equation. Those rationally decaying solutions in all space directions exhibit two kinds of characters, i.e., bright lump wave (one peak and two valleys) and bright–dark lump wave (one peak and one valley). In addition, we also obtain three families of bright–dark lump wave solutions to the nonlinear p-SK equation for $$p=3$$ .

Global exponential stability for quaternion-valued recurrent neural networks with time-varying delays

Abstract: In this paper, we employ a novel method for solving the problem of the global exponential stability of quaternion-valued recurrent neural networks (QVNNs) with time-varying delays. Theoretically, a QVNN can be separated into four real-valued systems, forming an equivalent real-valued system. From the view of matrix measure, based on Halanay inequality instead of Lyapunov function, some sufficient conditions are derived to guarantee the global exponential stability for QVNNs. Moreover, the activation functions are not assumed to be derivative any more, which makes the analytical procedure compact. Finally, a numerical example is provided to validate the advantage of the proposed method and to show the effectiveness of the main results.

An image encryption scheme combining chaos with cycle operation for DNA sequences

Abstract: An image encryption scheme is proposed using high-dimensional chaotic systems and cycle operation for DNA sequences. In the scheme, the pixels of the original image are encoded randomly with the DNA coding rule controlled by a key stream produced from Chen’s hyper-chaos. In addition to confusion on the DNA sequence matrix with Lorenz system, a cycle operation for DNA sequences is projected to diffuse the pixel values of the image. In order to enhance the diffusion effect, a bitwise exclusive-OR operation is carried out for the decoded matrices with a binary key stream, and then the cipher-image is obtained. Simulation results demonstrate that the proposed image encryption scheme with acceptable robustness is secure against exhaustive attack, statistical attack and differential attack.

Analytic solutions for the generalized complex Ginzburg–Landau equation in fiber lasers

Abstract: Generalized complex Ginzburg–Landau equation (GCGLE) can be used to describe the nonlinear dynamic characteristics of fiber lasers and has riveted much attention of researchers in ultrafast optics. In this paper, analytic solutions of the GCGLE are obtained via the modified Hirota bilinear method. Kink waves and period waves are presented by selecting the relevant parameters. The influence of the related parameters on them is analyzed and studied. The results indicate that the desired pulses can be demonstrated by effectively controlling the dispersion and nonlinearity of fiber lasers.

Two-dimensional localized Peregrine solution and breather excited in a variable-coefficient nonlinear Schrödinger equation with partial nonlocality

Abstract: Hierarchies of Peregrine solution and breather solution are derived in a (2+1)-dimensional variable-coefficient nonlinear Schrodinger equation with partial nonlocality. Based on these solutions, we study the control of the excitation of Peregrine solution and breather solution in different planes. In particular, the localized Peregrine solution and breather solution are firstly reported in two-dimensional space. It is expected that our analysis and results may give new insight into higher-dimensional localized rogue waves in nonlocal media.

A novel approach for strong S-Box generation algorithm design based on chaotic scaled Zhongtang system

Abstract: Substitution Box (S-Box) is one of the most significant structures used to create an encryption which is strong and resistant against attacks in block encryption algorithms. S-Box plays an important role in data encryption. This paper presents a novel S-Box generation algorithm design based on scaled Zhongtang chaotic system. In this study, a new random number generator which uses the new scaled Zhongtang chaotic system with very complicated and interesting dynamic features is designed; also, a new effective and strong S-Box design algorithm utilizing this RNG (random number generator) is developed. Bits generated by RNG are put to NIST tests and they passed all the NIST tests. Non-linearity, bit independence criteria, strict avalanche criteria, differential approximation probability performance tests are run on the proposed S-Box produced by new S-Box design algorithm. The proposed S-Box is compared with other studies available in the literature, and it is proved stronger and more effective.

Sampled-data-based lag synchronization of chaotic delayed neural networks with impulsive control

Abstract: In the framework of sampled-data control, this paper deals with the lag synchronization of chaotic neural networks with time delay meanwhile taking the impulsive control into account. By constructing a proper Lyapunov function and employing the impulsive control theory, some sufficient conditions for lag synchronization of the addressed chaotic neural networks are derived in terms of linear matrix inequalities (LMIs). The hybrid controller including sampled-data controller and impulsive controller is designed based on the established LMIs. A numerical example is provided to demonstrate the effectiveness and advantage of the obtained results.

Recursive parameter identification of the dynamical models for bilinear state space systems

Abstract: This paper investigates the recursive parameter and state estimation algorithms for a special class of nonlinear systems (i.e., bilinear state space systems). A state observer-based stochastic gradient (O-SG) algorithm is presented for the bilinear state space systems by using the gradient search. In order to improve the parameter estimation accuracy and the convergence rate of the O-SG algorithm, a state observer-based multi-innovation stochastic gradient algorithm and a state observer-based recursive least squares identification algorithm are derived by means of the multi-innovation theory. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed algorithms.

Secure communication in wireless sensor networks based on chaos synchronization using adaptive sliding mode control

Abstract: Due to resource constraints in wireless sensor networks and the presence of unwanted conditions in communication systems and transmission channels, the suggestion of a robust method which provides battery lifetime increment and relative security is of vital importance. This paper considers the secure communication in wireless sensor networks based on new robust adaptive finite time chaos synchronization approach in the presence of noise and uncertainty. For this purpose, the modified Chua oscillators are added to the base station and sensor nodes to generate the chaotic signals. Chaotic signals are impregnated with the noise and uncertainty. At first, we apply the modified independent component analysis to separate the noise from the chaotic signals. Then, using the adaptive finite-time sliding mode controller, a control law and an adaptive parameter-tuning method is proposed to achieve the finite-time chaos synchronization under the noisy conditions and parametric uncertainties. Synchronization between the base station and each of the sensor nodes is realized by multiplying a selection matrix by the specified chaotic signal which is broadcasted by the base station to the sensor nodes. Simulation results are presented to show the effectiveness and applicability of the proposed technique.

A novel method for designing S-box based on chaotic map and Teaching–Learning-Based Optimization

Abstract: A new method for obtaining strong S-boxes based on chaotic map and Teaching–Learning-Based Optimization (TLBO) is presented in this paper. Our method presents eight rounds; each round contains two transformations: row left shifting and columnwise rotation. The vectors for the transformations are different from one round to another, and they are controlled by two keys to the logistic map. These two keys are optimized by using TLBO which aims to construct a strong S-box that satisfies to the criteria set in advance. Test for the following criteria such as bijectivity, nonlinearity, strict avalanche criteria, equiprobable inputs/outputs XOR distribution is analyzed. Additionally, we will provide many comparisons with other S-boxes and test of the sensitivity to keys. The results of performance test show that the proposed design S-boxes presents good cryptography proprieties and can resist to several attacks.

Finite-time real combination synchronization of three complex-variable chaotic systems with unknown parameters via sliding mode control

Abstract: The problem of real combination synchronization between three complex-variable chaotic systems with unknown parameters is investigated by nonsingular terminal sliding mode control in a finite time. Based on the adaptive laws and finite-time stability theory, a nonsingular terminal sliding mode control is designed to ensure the real combination synchronization of three complex-variable chaotic systems in a given finite time. It is theoretically gained that the introduced sliding mode technique has finite-time convergence and stability in both arriving and sliding mode phases. Numerical simulation results are given to show the effectiveness and reliability of the finite-time real combination synchronization.

A novel method of S-box design based on discrete chaotic map

Abstract: A new method for obtaining random bijective S-boxes based on discrete chaotic map is presented. The proposed method uses a discrete chaotic map based on the composition of permutations. The obtained S-boxes have been tested on the number of criteria, such as bijection, nonlinearity, strict avalanche criterion, output bits independence criterion, equiprobable input/output XOR distribution and maximum expected linear probability. The results of performance test show that the S-box presented in this paper has good cryptographic properties. The advantage of the proposed method is the possibility to achieve large key space, which makes it suitable for generation of $$n\times n$$ S-boxes for larger values of n. Also, because this method uses discrete chaotic map based on the composition of permutations which has finite space domain, there is no need for discretization of continuous values of chaotic map, so the process of generation of S-boxes is not affected by approximations of any kind.

Constructing chaotic systems with conditional symmetry

Abstract: Asymmetric dynamical systems sometimes admit a symmetric pair of coexisting attractors for reasons that are not readily apparent. This phenomenon is called conditional symmetry and deserves further explanation and exploration. In this paper, a general method for constructing such systems is proposed in which the asymmetric system restores its original equation when some of the variables are subjected to a symmetric coordinate transformation combined with a special offset boosting. Two regimes of this conditional symmetry are illustrated in chaotic flows where a symmetric pair of attractors resides in asymmetric basins of attraction.

Nonlinear vibration of functionally graded graphene-reinforced composite laminated beams resting on elastic foundations in thermal environments

Abstract: Modeling and nonlinear vibration analysis of graphene-reinforced composite (GRC) laminated beams resting on elastic foundations in thermal environments are presented. The graphene reinforcements are assumed to be aligned and are distributed either uniformly or functionally graded of piece-wise type along the thickness of the beam. The motion equations of the beams are based on a higher-order shear deformation beam theory and von Karman strain displacement relationships. The beam–foundation interaction and thermal effects are also included. The temperature-dependent material properties of GRCs are estimated through a micromechanical model. A two-step perturbation approach is employed to determine the nonlinear-to-linear frequency ratios of GRC laminated beams. Detailed parametric studies are carried out to investigate the effects of material property gradient, temperature variation, stacking sequence as well as the foundation stiffness on the linear and nonlinear vibration characteristics of the GRC laminated beams.

Multistability analysis, circuit implementations and application in image encryption of a novel memristive chaotic circuit

Abstract: A novel memristive chaotic circuit is proposed by replacing the Chua’s diode in modified Chua’s circuit with a smooth active memristor, and the corresponding memristive model is analyzed and validated. The equilibrium point set, dissipativity and stability of this new chaotic circuit are developed theoretically. The dynamic characteristics for the new system are presented by means of phase diagrams, Lyapunov exponents, bifurcation diagrams and Poincare maps. The coexistence of the memristive system is carried out from the perspective of asymmetric coexistence and symmetry coexistence. In addition, the coexistence of multiple states is studied by a more direct method with initial value as the system variable to gain a more intuitive observation. The circuit model of the memristive chaotic system is designed through Multisim simulation software. Finally, the memristive chaotic sequence is used to encrypt the image, and the influence of multistability on the encryption is investigated by the histogram, correlation and key sensitivity. The results show that the proposed new memristive chaotic system has high security.

Dynamics of light bullets in inhomogeneous cubic-quintic-septimal nonlinear media with {\varvec{{\mathcal {PT}}}}-symmetric potentials

Abstract: A (3+1)-dimensional nonlinear Schrodinger equation with variable-coefficient dispersion/diffraction and cubic-quintic-septimal nonlinearities is studied, two families of analytical light bullet solutions with two types of $${{\mathcal {PT}}}$$ -symmetric potentials are obtained. The coefficient of the septimal nonlinear term strongly influences the form of light bullet. The direct numerical simulation indicates that light bullet solutions in different cubic-quintic-septimal nonlinear media exhibit different property of stability, and under different $${\mathcal {PT}}$$ -symmetric potentials they also show different stability against white noise. These stabilities of evolution originate from subtle interplay among dispersion, diffraction, nonlinearity and $${\mathcal {PT}}$$ -symmetric potential. Moreover, compression and expansion of light bullets in the hyperbolic dispersion/diffraction system and periodic modulation system are investigated numerically. The evolution of light bullet in periodic modulation system is more stable than that in the hyperbolic dispersion/diffraction system.