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Electromagnetic induction plays a key role in regulating the electrical activity, excitability, and bistable structure of neurons. In this paper, a discontinuous control strategy with membrane potential as the threshold is introduced to the HR neuron model under the influence of electromagnetic field (EMFN model), and then we establish a Filipov EMFN neuron model to realize the regulation effect of electromagnetic field on the neuron system. Specific work of this paper reads as follows: first, the existence and stability of equilibrium points of two subsystems are analyzed by using MatCont software; second, the bistable region and its internal mechanism are discussed in detail by two-parameter bifurcation analysis; third, the mechanism of bistability and a series of complex sliding mode dynamics including sliding segment and sliding bifurcations are further revealed with the help of the fast–slow variable dissection method; finally, based on Hamilton energy, the regulation of threshold on chaotic discharge in the Filippov EMFN neuron model is explored. The numerical simulation results show that the EMFN neuron model can produce the corresponding sliding limit cycle and sliding bursting behaviors under the influence of the threshold control strategy, meanwhile, the chaotic behavior of the new system can be controlled effectively within a certain range. The results provide ideas for controlling the effects of electromagnetic fields on the biological neuronal system and exploring the regulation mechanism of neurological diseases. [ABSTRACT FROM AUTHOR]

In this paper, the chaotic phenomenon is reported in a bearing system. The chaotic dynamics of the new system is first derived from an available bearing system. The proposed system is then analyzed using various tools to observe its dynamical behaviors. Theoretical and simulation results confirm the presence of chaotic and periodic behaviors in the new bearing system. [ABSTRACT FROM AUTHOR]

In this paper, we have designed a rhombic microchannel plane micromixer (RMPM). The RMPM uses the principle of converging and diverging to improve the mixing efficiency. We improved the mixing efficiency by changing the rhombic angles and the rhombic channel width ratios. The influence of geometric parameters on mixing efficiency is analyzed by control of the variable method. Through the analysis of the numerical simulation, the RMPM can help increase the chaotic convection between different concentrations of fluids. The results of the study show that the rhombic angle and the width ratio of a microchannel can have a considerable effect on the mixing efficiency. The micromixer can be potentially useful in the future applications of rapid and high throughput mixing. [ABSTRACT FROM AUTHOR]

This paper offers two different attacks on a freshly proposed image encryption based on chaotic logistic map. The cryptosystem under study first uses a secret key of 80-bit and employed two chaotic logistic maps. We derived the initial conditions of the logistic maps from using the secret key by providing different weights to all its bits. Additionally, in this paper eight different types of procedures are used to encrypt the pixels of an image in the proposed encryption process of which one of them will be used for a certain pixel which is determined by the product of the logistic map. The secret key is revised after encrypting each block which consisted of 16 pixels of the image. The encrypting process have weakness, worst of which is that every byte of plaintext is independent when substituted, so the cipher text of the byte will not change even the other bytes have changed. As a result of weakness, a chosen plaintext attack and a chosen cipher text attack can be completed without any knowledge of the key value to recuperate the ciphered image. [ABSTRACT FROM AUTHOR]

In the present paper, we report on the switching dynamics of both single and coupled VO2-based oscillators, with resistive and capacitive coupling, and explore the capability of their application in oscillatory neural networks. Based on these results, we further select an adequate SPICE model to describe the modes of operation of coupled oscillator circuits. Physical mechanisms influencing the time of forward and reverse electrical switching, that determine the applicability limits of the proposed model, are identified. For the resistive coupling, it is shown that synchronization takes place at a certain value of the coupling resistance, though it is unstable and a synchronization failure occurs periodically. For the capacitive coupling, two synchronization modes, with weak and strong coupling, are found. The transition between these modes is accompanied by chaotic oscillations. A decrease in the width of the spectrum harmonics in the weak-coupling mode, and its increase in the strong-coupling one, is detected. The dependences of frequencies and phase differences of the coupled oscillatory circuits on the coupling capacitance are found. Examples of operation of coupled VO2 oscillators as a central pattern generator are demonstrated. [ABSTRACT FROM AUTHOR]

Quantum key distribution (QKD) promises unconditionally secure communications, however, the low bit rate of QKD cannot meet the requirements of high-speed applications. Despite the many solutions that have been proposed in recent years, they are neither efficient to generate the secret keys nor compatible with other QKD systems. This paper, based on chaotic cryptography and middleware technology, proposes an efficient and universal QKD protocol that can be directly deployed on top of any existing QKD system without modifying the underlying QKD protocol and optical platform. It initially takes the bit string generated by the QKD system as input, periodically updates the chaotic system, and efficiently outputs the bit sequences. Theoretical analysis and simulation results demonstrate that our protocol can efficiently increase the bit rate of the QKD system as well as securely generate bit sequences with perfect statistical properties. Compared with the existing methods, our protocol is more efficient and universal, it can be rapidly deployed on the QKD system to increase the bit rate when the QKD system becomes the bottleneck of its communication system. [ABSTRACT FROM AUTHOR]

This paper puts forward a novel image encryption algorithm that is based on permutation-diffusion architecture. In pixels' permutation stage, algorithm takes full advantage of the idea of magic cube's scrambling. There is only simple cyclic shift operation in each sub-block's permutation, but when the algorithm has disposed the current sub-block, the adjacent sub-blocks will be dealt with, too. In the cyclic shift of each row, stable points will help to decrease the correlation of adjacent pixels. To make encryption procedure uncertain, this paper brings in a parameter named delay-time that is generated by chaotic map. In the diffusion stage, by combining multiple operations and dynamic look-up table together, the proposed algorithm highly increases the uncertainty of the encryption procedure. At last, the experiment results of key space analysis, information entropy analysis, histogram analysis and etc. show that the encryption algorithm has well performance and it can be used in image encryption and transmission. [ABSTRACT FROM AUTHOR]

In this paper, based on the idea of nonlinear observer, lag synchronization of chaotic fractional system with commensurate and incommensurate order is studied by the stability theorem of linear fractional-order systems. The theoretical analysis of fractional-order systems in this paper is a systematic method. This technique is applied to achieve the lag synchronization of fractional-order Rössler's system, verified by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper studies chaos synchronization via unidirectional coupling. The self-synchronization of Lorenz systems, modified coupled dynamos systems and hyperchaotic Chen systems is studied by three methods: the Lyapunov function method, the global synchronization method and the numerical calculation of the largest Lyapunov exponent method. In regard to application to communication, we show that via transmitting single signal the synchronization of the drive system and the response system can be achieved. An example of applying self-synchronization of hyperchaotic Chen systems to chaotic masking secure communication is presented in this paper. Simulation results show the effectiveness of the method. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behavior of a non-symmetric double potential well in a tilted magnetic field is studied. The classical Poincare section is given to exhibit the chaotic behavior of the system, and non-linear resonant lead to chaos. The paper has also given the energy spectral statistics which satisfies Brody's distribution, tunnelling effect develops quantum chaos and also holds back the development of chaos. [ABSTRACT FROM AUTHOR]

In this paper, we propose a dynamic delayed feedback control approach or desynchronization of chaotic-bursting synchronous activities in an ensemble of globally coupled neuronal oscillators. We demonstrate that the difference signal between an ensemble's mean field and its time delayed state, filtered and fed back to the ensemble, can suppress the self-synchronization in the ensemble. These individual units are decoupled and stabilized at the desired desynchronized states while the stimulation signal reduces to the noise level. The effectiveness of the method is illustrated by examples of two different populations of globally coupled chaotic-bursting neurons. The proposed method has potential for mild, effective and demand-controlled therapy of neurological diseases characterized by pathological synchronization. [ABSTRACT FROM AUTHOR]

In this paper, on the basis of the Laypunov stability and the cascade synchronization approach, an effectual scroll controller and improving cascade synchronization approach are derived. The chaotic attractor can be displayed to be lopsided, till to be 1-scroll and periodic via the different scroll controller. And the proposed synchronization technique is applied to the new system, which the synchronization controller obtained by improving cascade method and adaptive functions. Numerical results are used to verify the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

In this paper, we present a selective image encryption system based on couple spatial chaotic systems, the cascade one-dimensional Logistic map and high-dimensional spatial chaotic system has been used to generate the adequate encryption sequence, then the selective gray-level image encryption is implemented with the sequence, which can greatly improve the encryption performance and efficiency. In addition, we also adopt an index array to control the generation of the secret key, a completely different cipher text will be obtained if a pixel's value is altered in the original image, which can resist the differential attack effectively. [ABSTRACT FROM AUTHOR]

In this paper, active control and adaptive control methods are applied, respectively. Adaptive control method is implemented when system parameters are unknown and active control method is applied when system parameters are known. Based on the Lyapunov stability theory, the controllers are designed to realize anti-synchronization, meanwhile, the update laws of parameters are proposed. The theoretical proof is given. And two groups of examples are shown to verify the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

In recent years, a lot of chaotic cryptosystems have been proposed. However, most of these cryptosystems can encrypt only one plaintext in one encryption process. We call these cryptosystems single-plaintext-oriented cryptosystems. In this paper, the authors propose a new chaotic cryptosystem which can encrypt multiple plaintexts in one encryption process. The proposed cryptosystem is dedicated to encrypting multiple plaintexts in the situation of transmitting multiple secret files over public data communication network in one secure transmission. Experiments and theoretic analysis show that the proposed cryptosystem possesses high security and fast performance speed. They also show that the proposed cryptosystem is more secure than single-plaintext-oriented chaotic cryptosystems in this special situation. [ABSTRACT FROM AUTHOR]

In this paper, a chaotic synchronization scheme is proposed to achieve adaptive synchronization between a novel hyperchaotic system and the hyperchaotic Chen system with fully unknown parameters. Based on the Lyapunov stability theory, an adaptive controller and parameter updating law are presented to synchronize the above two hyperchaotic systems. The corresponding theoretical proof is given and numerical simulations are presented to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Aiming at the drawbacks of the chaotic masking scheme, this paper optimizes this conventional scheme by using improved state observer method and system-alternating method, proposes a new secure communication scheme which can improve these drawbacks of chaotic method: (1) Restriction that the power of useful signal must be smaller than that of chaotic signal. (2) Low security. In addition, the model of this whole communication system is constructed under the system simulation environment of Simulink. [ABSTRACT FROM AUTHOR]

In this paper, a chaotic synchronization scheme is proposed to achieve the generalized synchronization between two different fractional-order chaotic systems. Based on the stability theory of fractional-order systems and the pole placement technique, a controller is designed and theoretical proof is given. Two groups of examples are shown to verify the effectiveness of the proposed scheme, the first one is to realize the generalized synchronization between the fractional-order Chen system and the fractional-order Rössler system, the second one is between the fractional-order Lü system and the fractional-order hyperchaotic Lorenz system. The corresponding numerical simulations verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper presents the general method for the adaptive function Q-S synchronization of different chaotic (hyper-chaotic) systems. Based upon the Lyapunov stability theory, the dynamical evolution can be achieved by the Q-S synchronization with a desired scaling function between the different chaotic (hyper-chaotic) systems. This approach is successfully applied to two examples: Chen hyper-chaotic system drives the Lorenz hyper-chaotic system; Lorenz system drives Lü hyper-chaotic system. Numerical simulations are used to validate and demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

An epidemic spreading through an adaptive network, where the susceptible are able to avoid contact with the infective by rewiring their network connections, with random and regular contacts is considered. This paper uses a new mathematical model obtained by pair approximation to explore the effect of rewiring of the epidemic dynamics. We show that chaotic behavior can emerge while considering rewiring. The obtained results show that rewiring plays an very important role on the dynamical behavior of the epidemic model. [ABSTRACT FROM AUTHOR]

This paper studies the problem of chaos synchronization between two different hyperchaotic systems with uncertain parameters. Based on the Lyapunov stability theory, we obtain the sufficient condition of synchronization between two different hyperchaotic systems with uncertain parameters. A new adaptive controller with parameter update laws is designed to synchronize these chaotic systems. We proved it in theory with an uncertain hyperchaotic Lorenz system and an uncertain hyperchaotic Rössler system. Numerical results verified the validation of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper studied the dynamic behavior of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system, then numerical analysis of the different fractional orders hyper-chaotic systems are carried out under the predictor-corrector method. We proved the two systems are in hyper-chaos when the maximum and the second largest Lyapunov exponential are calculated. Also the smallest orders of the systems are proved when they are in hyper-chaos. The diverse structure synchronization of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system is realized using active control method. Numerical simulations indicated that the scheme was always effective and efficient. [ABSTRACT FROM AUTHOR]

This paper deals with the finite-time chaos synchronization of a new hyperchaotic Lorenz system. Based on the finite-time stability theory, a simple and robust controller is proposed to realize finite-time chaos synchronization for the hyperchaotic Lorenz system. Theoretical analysis proved that the scheme can ensure the error system globally finite-time stable. Numerical simulations are provided to show the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

This paper investigates the global synchronization problem of master-slave coupled multi-scroll saturated chaotic systems via single-state linear feedback control. An algebraic criterion for global synchronization is rigorously proven by means of the absolute stability theory. The obtained algebraic criterion is then optimized thereby deriving a less-conservative result, which is finally verified by numerical examples. [ABSTRACT FROM AUTHOR]

Such a problem, how to resolve the problem of long-term unpredictability of chaotic systems, has puzzled researchers in nonlinear research fields for a long time during the last decades. Recently, Voss et al. had proposed a new scheme to research the anticipating synchronization of integral-order nonlinear systems for arbitrary initial values and anticipation time. Can this anticipating synchronization be achieved with hyper-chaotic systems? In this paper, we discussed the application of anticipating synchronization in hyper-chaotic systems. Setting integer order and commensurate fractional order hyper-chaotic Chen systems as our research objects, we carry out the research on anticipating synchronization of above two systems based on analyzing the stability of the error system with the Krasovskill-Lyapunov stability theory. Simulation experiments show anticipating synchronization can be achieved in both integer order and fractional order hyper-chaotic Chen system for arbitrary initial value and arbitrary anticipation time. [ABSTRACT FROM AUTHOR]

In order to solve the problem of degradation of dynamical properties caused by finite states of computer, a new binary stream-cipher algorithm based on dual one-dimensional chaotic maps is proposed in this paper. In the process of generation, we employ a parameter of one chaotic map to perturb the other chaotic map's trajectory to lengthen the cycle-length of the other chaotic map's trajectory. In addition, we design a nonlinear principle to generate a pseudo-random chaotic bit sequence as key stream. Statistic proprieties show that the sequence is of high randomness. [ABSTRACT FROM AUTHOR]

Based on the stability theory of fractional order systems and the pole placement technique, this paper designs a synchronization scheme with the state observer method and achieves the projective synchronization of a class of fractional order chaotic systems. Taking an example for the fractional order unified system by using this observer controller, and numerical simulations of fractional order Lorenz-like system, fractional order Lü system and fractional order Chen system are provided to demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, an image encryption algorithm based on couple multiple chaotic systems is presented. It made the one-dimensional Coupled Map Lattice (CML) formed by Skew Tent map as spatiotemporal chaotic system and made its output sequence as the initial value of logistic and meanwhile did iterative of specific times to get the final key sequence, and then did XOR operations with corresponding pixels to finish the encryption. Numerical analysis expresses that this algorithm has large enough space and high security. [ABSTRACT FROM AUTHOR]

Projective synchronization investigates the synchronization of systems evolve in same orientation, however, in practice, the situation of same orientation is only minority, and the majority is different orientation. This paper investigates the latter, proposes the concept of rotating synchronization, and verifies its necessity and feasibility via theoretical analysis and numerical simulations. Three conclusions were elicited: first, in three-dimensional space, two arbitrary nonlinear chaotic systems who evolve in different orientation can realize synchronization at end; second, projective synchronization is a special case of rotating synchronization, so, the application fields of rotating synchronization is more broadly than that of the former; third, the overall evolving information can be reflected by single state variable's evolving, it has self-similarity, this is the same as the basic idea of phase space reconstruction method, it indicates that we got the same result from different approach, so, our method and the phase space reconstruction method are verified each other. [ABSTRACT FROM AUTHOR]

This paper analyzes the synchronizations for autonomous chaotic systems with disturbance of parameter, achieves the self-synchronization of Lü system, a modified coupled dynamos system and a four-dimensional hyperchaotic system by the methods of active control and adaptive parameter. In addition, the synchronization of Lorenz system and Chen system is presented. Numerical simulations are provided for illustration and verification of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the generalized synchronization of hyperchaos systems, and a new method, by which adaptive generalized synchronization of chaotic systems with a kind of linear and nonlinear relationship between the drive and response systems can be achieved, is proposed. This new method has more extensive application scope. Based on the Lyapunov stability theory, the correctness of the proposed scheme is strictly demonstrated. It is also illustrated by applications to hyperchaotic Chen system and hyperchaotic Lorenz system and the simulation results show the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper studies full state hybrid projective synchronization of the unified chaotic system with unknown parameters. Based on the Lyapunov stability theory, an adaptive controller is designed. It is proved theoretically that the controller can make the states of the dynamical system and the response system with unknown parameters asymptotically full state hybrid projective synchronized. Numerical simulations show the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

In this paper, we have proposed a novel three-dimensional Lorenz-like chaotic system. Some basic properties of the system, such as dynamical behaviors, bifurcation diagram. Lyapunov exponents and Poincare mapping are investigated either analytically or numerically. Furthermore, the control problem of the new chaotic system was studied via nonlinear backstepping method. The single backstepping control input was designed according to Lyapunov stability criterion. Numerical simulations are carried out in order to demonstrate the effectiveness of the proposed control design. [ABSTRACT FROM AUTHOR]

This paper proposes a new block encryption algorithm. The chaotic trajectories are computed by weighting. Then the result is used to mask the plaintext. Multiple blocks of plaintext are encrypted at the same time and this decreases the chaotic iterations. So the encryption speed is improved to some extent. The proposed algorithm is flexible. When the number of weights is increased, the number of the encrypted plaintext block at the same time is increased and the encryption speed is improved. The simulation result shows that the proposed algorithm has fast encryption speed and fine security. [ABSTRACT FROM AUTHOR]

The impulsive synchronization of two chaotic Chen-Lee systems was investigated in this paper. Based on Lyapunov's direct method, sufficient conditions for the global exponential synchronization and global asymptotical synchronization were derived. Further, the theoretical results were verified by a numerical simulation. In addition, the impulsive synchronization of two chaotic Chen-Lee systems was also implemented using an electronic circuit. [ABSTRACT FROM AUTHOR]

In this paper, we propose an algorithm for one-way hash function construction based on the chaotic look-up table with changeable parameter. First, the original message with padding is divided into block messages as groups and then further broken into sub-block messages, which are translated into corresponding ASCII codes by groups. Then the group ASCII codes are successively inputted into the chaotic look-up table updated by changeable parameter to permute corresponding values. Finally, based on the calculation of the values, 128-bit hash value is generated. Performance analysis indicates that our proposed algorithm satisfies sensitive requirements and can resist all kinds of attacks. [ABSTRACT FROM AUTHOR]

In this paper, a shell model for the energy cascade in three-dimensional turbulence at varying the viscosity is studied. When the viscosity parameter ν is large enough, the phase orbit of each shell in the system is a stable fixed point. As ν diminishes down to a critical value, the point becomes unstable and a stable periodic orbit appears via a supercritical Hopf bifurcation. For the quasiperiodic solution of the system, each shell has a own dynamic behavior. At ν = 6.88×10-5, the system initiates a complex scenario of bifurcations, where the phase orbits of un and un+3 begin to form a intersected section. Farther decreasing ν, we observe a transition from quasiperiodic solution to chaos through a sequence of Neimark-Sacker bifurcations. The behaviors can be vividly shown in the change of the average energy function E with ν. At last, the transition to chaos in the ν-δ parameter space is also obtained. [ABSTRACT FROM AUTHOR]

Unidirectional coupled synchronization of two identical or different chaotic systems has been carefully studied based on the master-slave synchronization scheme, where the synchronous state is that of the master system and cannot be changed after they realized synchronization. In this paper, a general bidirectional synchronization scheme is presented which made the master-slave scheme a special case. It is straightforward to tune the synchronous state by just changing the value of a parameter. Based on the general bidirectional synchronization scheme, active control method is used to tune the synchronous state of two pairs of different chaotic systems: the Lorenz and Chen systems; and then the Lü and Rössler systems. [ABSTRACT FROM AUTHOR]

In this paper, the impulsive synchronization of hyperchaotic Lü systems is discussed. The sufficient conditions on feedback strength and impulsive interval are established to guarantee the synchronization. The method is proved true by Lyapunov stability theory. In addition, a scheme of impulsive synchronization via transmitting single signal is presented. Numerical simulations show the effectiveness of the methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new adaptive synchronization method, called a fuzzy adaptive delayed feedback synchronization (FADFS) method, for time-delayed chaotic systems with uncertain parameters. An FADFS controller that is based on the Lyapunov-Krasovskii theory, Takagi-Sugeno (T-S) fuzzy model, and delayed feedback control is developed to guarantee adaptive synchronization. The proposed controller can be obtained by solving the linear matrix inequality (LMI) problem. A numerical example using a time-delayed Lorenz system is discussed to assess the validity of the proposed FADFS method. [ABSTRACT FROM AUTHOR]

In this paper, periodic parametric perturbations are used to control chaos in Liu system. By changing the frequency of the perturbation signal, Liu system can be guided to not only periodic motion but also hyperchaos. Phase diagram, bifurcation diagram, Lyapunov exponents spectrum and Poincáre map are used to analyze the dynamic behavior of the controlled system in the numerical simulations, which show the effectiveness of our method. [ABSTRACT FROM AUTHOR]

In this paper, the drive system and the response system can be in a state of linear generalized synchronization via transmitting single signal. By means of a transitional system, the response system is obtained by variable replacement method. Chen system and hyperchaotic Chen system are used as examples in numerical simulations. Simulation results show the effectiveness of the method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new $\mathcal{H}_{\infty}$ lag synchronization scheme for a general class of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) approach, the $\mathcal{H}_{\infty}$ lag synchronization controller is presented to not only guarantee exponential lag synchronization but also reduce the effect of external disturbance to an $\mathcal{H}_{\infty}$ norm constraint. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. As an application of the proposed method, the $\mathcal{H}_{\infty}$ lag synchronization problem for Genesio-Tesi system is investigated. [ABSTRACT FROM AUTHOR]

The Šil'nikov homoclinic theorem provides one analytic criterion for proving the existence of chaos in three-dimensional autonomous nonlinear systems. In applications of the theorem, however, the existence of a homoclinic orbit that usually determines the geometric structure of the chaotic attractor is not easily verified mainly because there are no available efficient methods. In this paper, based on the undetermined coefficient approach we present a framework of how to find homoclinic orbits in two classes of three-dimensional autonomous nonlinear systems of normal forms, including how to set a reasonable form of expanding series of the homoclinic orbit, how to determine all coefficients in the expansion, and how to find a numerical homoclinic orbit. Numerical examples show that the proposed framework in combination with computer simulation is very efficient. [ABSTRACT FROM AUTHOR]

Synchronization of multiple identical chaotic systems, coupled in a ring structure, was studied in this paper. Ueda attractor was used as an example to perform the synchronization of several chaotic systems. The bound of the Ueda attractor was also estimated by numerical simulation. The above results were also adopted to design a controller to synchronize chaotic systems. The stability of the synchronization of multiple identical chaotic systems was investigated using Lyapunov's direct method. Some sufficient conditions of asymptotical synchronization were attained from rigorous mathematical theory. Further, numerical results were also demonstrated in order to validate the proposed synchronization approach. [ABSTRACT FROM AUTHOR]

This paper studies synchronization between two linearly coupled non-autonomous chaotic systems with parameter mismatches. Based on Lyapunov's stability theory and Sylvester's criterion, some algebraic criteria are derived to synchronize the master and slave system with error bound. Besides, the largest synchronization error can be estimated analytically. Some numerical examples are presented to verify the effectiveness of these criteria. In the examples, the estimated largest synchronization error is compared with the evolution of the error variable, which further shows that the present techniques are effective. [ABSTRACT FROM AUTHOR]

An analysis on the chaotic dynamics of a six-dimensional nonlinear system which represents the averaged equation of an axially moving viscoelastic belt is given in this paper for the first time. We combine the theory of normal form and the global perturbation method to investigate the global bifurcations and chaotic dynamics of the axially moving viscoelastic belt. Firstly, the theory of normal form is used to reduce six-dimensional averaged equation to the simpler normal form. Then, the global perturbation method is employed to analyze the global bifurcations and chaotic dynamics of six-dimensional nonlinear system. The analysis results indicate that there exist the homoclinic bifurcations and the single-pulse in six-dimensional averaged equation. Finally, numerical simulations are also used to investigate the nonlinear dynamic characteristics of the axially moving viscoelastic belt. The results of numerical simulations demonstrate that there exist the chaotic motions and the jumping orbits of the axially moving viscoelastic belt. [ABSTRACT FROM AUTHOR]

oActive sliding mode control is one of the effective methods to synchronize chaotic systems in the presence of uncertainties. Use of the method, however, requires decision making on how to choose the control parameters for a specific performance. In this paper we propose an algorithm to determine the best control parameters for which the minimum control efforts are required to synchronize two identical or non-identical chaotic systems. We have also determined the maximum range of the uncertainties on which the selected control parameters to work properly. The effectiveness of the proposed method has been verified through numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a master-slave synchronization scheme of two n-dimensional nonautonomous chaotic systems coupled by sinusoidal state error feedback control, where parameter mismatch exists between the external harmonic excitation of master system and that of slave one. A concept of synchronization with error bound is introduced due to parameter mismatch, and then the bounds of synchronization error are estimated analytically. Some synchronization criteria are firstly obtained in the form of matrix inequalities by the Lyapunov direct method, and then simplified into some algebraic inequalities by the Gerschgorin disc theorem. The relationship between the estimated synchronization error bound and system parameters reveals that the synchronization error can be controlled as small as possible by increasing the coupling strength or decreasing the magnitude of mismatch. A three-dimensional gyrostat system is chosen as an example to verify the effectiveness of these criteria, and the estimated synchronization error bounds are compared with the numerical error bounds. Both the theoretical and numerical results show that the present sinusoidal state error feedback control is effective for the synchronization. Numerical examples verify that the present control is robust against amplitude or phase mismatch. [ABSTRACT FROM AUTHOR]

In this paper, a novel approach for generating multi-wing chaotic attractors via switching control is proposed. By using a switching controller, multi-wing chaotic attractors can be generated from a double-wing system. The presented method is different from that of classical multi-scroll chaotic attractors generated by odd-symmetric multi-segment linear functions from Chua system. Furthermore, the basic dynamical behaviors, including equilibrium points, maximum Lyapunov exponents and bifurcations, are further investigated. An improved module-based unified circuit is designed for realizing 4, 6, 8 and 10-wing chaotic attractors, and the experimental result is also demonstrated, which is consistent with the numerical simulation. [ABSTRACT FROM AUTHOR]