Image encryption with chaotically coupled chaotic maps

We present a novel secure cryptosystem for direct encryption of color images, based on chaotically coupled chaotic maps. The proposed cipher provides good confusion and diffusion properties that ensures extremely high security because of the chaotic mixing of pixels’ colors. Information is mixed and distributed over a complete image using a complex strategy that makes known plaintext attack unfeasible. The encryption algorithm guarantees the three main goals of cryptography: strong cryptographic security, short encryption/decryption time, and robustness against noise and other external disturbances. Due to the high speed, the proposed cryptosystem is suitable for application in real-time communication systems.     

Preserving synchronization under matrix product modifications

In this article we present a methodology under which stability and synchronization of a dynamical master/slave system configuration are preserved under modification through matrix multiplication. The objective is to show that under a defined multiplicative group, hyperbolic critical points are preserved along the stable and unstable manifolds. The properties of this multiplicative group were determined through the use of simultaneous Jordan decomposition. It is also shown that a consequence of this approach is the preservation of the signature of the Jacobian matrix associated with the dynamical system. To illustrate the results we present several examples of different modified systems.     

Dynamic Feedback Controlling Chaos in Current-Mode Boost Converter

A method for the control of chaos in the current-mode boost converter is presented by using the first-order dynamic feedback control. The feedback part consists of a resistance and a capacitance in series. The system to be controlled is treated as a third-order model, and then the discrete mapping model is obtained by using the data-sampling method. By analysing the position of the maximum norm eigenvalue, the stable range of feedback gain is ascertained out and its optimization is also carried out. Finally, the results of simulation and experiment confirm the correctness of the theoretical analysis and the validity of the proposed means.     

How many parameters can be identified by adaptive synchronization in chaotic systems?

Five interesting experiments have been done for a class of chaos synchronization systems with unknown parameters and unknown control directions. And three important conclusions about parameters identification have been made. First, a necessary and sufficient condition for parameters identification is obtained. Second, a Nussbaum method is proposed to solve the problem of unknown control direction. Third, the adaptive method is not infinitely effective considered for our current ability of computation and simulation algorithm.     

Synchronization in coupled nonidentical incommensurate fractional-order systems

Synchronization of fractional-order nonlinear systems has received considerable attention for many research activities in recent years. In this Letter, we consider the synchronization between two nonidentical fractional-order systems. Based on the open-plus-closed-loop control method, a general coupling applied to the response system is proposed for synchronizing two nonidentical incommensurate fractional-order systems. We also derive a local stability criterion for such synchronization behavior by utilizing the stability theory of linear incommensurate fractional-order differential equations. Feasibility of the proposed coupling scheme is illustrated through numerical simulations of a limit cycle system, a chaotic system and a hyperchaotic system.     

Cross-correlation between time series of vehicles and passengers

We study in this paper a cross-correlation between time series of vehicles and passengers collected in the ferry-boat system (sea route that connects the city of Salvador and Itaparica island, Bahia, Brazil), this study is based on the detrended cross-correlation analysis (DCCA) method. The DCCA method is designed to investigate power-law cross correlations between different simultaneously recorded time series in the presence of nonstationarity. Here in this paper we show that is possible to discriminate cross-correlation between vehicles and passengers and also identify seasonal components.     

Direct transition from a stable equilibrium to quasiperiodicity in non-smooth systems

The purpose of this Letter is to show how a border-collision bifurcation in a piecewise-smooth dynamical system can produce a direct transition from a stable equilibrium point to a two-dimensional invariant torus. Considering a system of nonautonomous differential equations describing the behavior of a power electronic DC/DC converter, we first determine the chart of dynamical modes and show that there is a region of parameter space in which the system has a single stable equilibrium point. Under variation of the parameters, this equilibrium may collide with a discontinuity boundary between two smooth regions in phase space. When this happens, one can observe a number of different bifurcation scenarios. One scenario is the continuous transformation of the stable equilibrium into a stable period-1 cycle. Another is the transformation of the stable equilibrium into an unstable period-1 cycle with complex conjugate multipliers, and the associated formation of a two-dimensional (ergodic or resonant) torus.     

Global synchronization in arrays of coupled networks with one single time-varying delay coupling

Global synchronization in arrays of coupled networks with one single time-varying delay coupling is investigated in this Letter. A general linear coupled network with a time-varying coupling delay is proposed and its global synchronization is further discussed. Some sufficient criteria are derived based on Lyapunov functional and linear matrix inequality (LMI). It is shown that under one single delay coupling, the synchronized state changes, which is different from the conventional synchronized solution. Moreover, the degree of the nodes and the inner delayed coupling matrix play key roles in the synchronized state. In particular, the derivative of the time-varying delay can be any given value. Finally, numerical simulations are given to illustrate the theoretical results.     

Different Types of Synchronization in Time-Delayed Systems

We investigate different types of synchronization between two unidirectionally nonlinearly coupled identical delay- differential systems related to optical bistable or hybrid optical bistable devices. This system can represent some kinds of delay-differential models, i.e. Ikeda model, Vall~e model, sine-square model, Mackey Glass model, and so on. We find existence and sufficient stability conditions by theoretical analysis and test the correctness by＂ numerical simulations. Lag, complete and anticipating synchronization are observed, respectively. It is found that the time-delay system can be divided into two parts~ one is the instant term and the other is the delay term. Synchronization between two identical chaotic systems can be derived by adding a coupled term to the delay term in the driven system.     

Stability analysis and design of amplitude death induced by a time-varying delay connection

The present Letter considers amplitude death in a pair of oscillators coupled by a time-varying delay connection. A linear stability analysis is used to derive the boundary curves for amplitude death in a connection parameters space. The delay time can be arbitrarily long for certain amplitude of delay variation and coupling strength. A simple systematic procedure for designing such variation and strength is provided. The theoretical results are verified by a numerical simulation.     

A Hyperchaotic Attractor with Multiple Positive Lyapunov Exponents

There are many hyperchaotic systems, but few systems can generate hyperchaotic attractors with more than three PLEs （positive Lyapunov exponents）. A new hyperchaotic system, constructed by adding an approximate time-delay state feedback to a five-dimensional hyperchaotic system, is presented. With the increasing number of phase-shift units used in this system, the number of PLEs also steadily increases. Hyperchaotic attractors with 25 PLEs can be generated by this system with 32 phase-shift units. The sum of the PLEs will reach the maximum value when 23 phase-shift units are used. A simple electronic circuit, consisting of 16 operational amplifiers and two analogy multipliers, is presented for confirming hyperchaos of order 5, i.e., with 5 PLEs.     

Self-Stable Chaos Control of dc-dc Converter

A new concept related to self-stable chaos control is first put forward, and its theoretical basis and realization are presented from the frequency-domain perspective. With a new analogous-circuit realization of this control its applications in the voltage-mode Buck converter is discussed. The harmonic-balance method is applied to determine the control range of the control parameter. The experiment results given in the last part confirm the validity of the proposed control method.     

Exponential decay and scaling laws in noisy chaotic scattering

In this Letter we present a numerical study of the effect of noise on a chaotic scattering problem in open Hamiltonian systems. We use the second order Heun method for stochastic differential equations in order to integrate the equations of motion of a two-dimensional flow with additive white Gaussian noise. We use as a prototype model the paradigmatic Hénon-Heiles Hamiltonian with weak dissipation which is a well-known example of a system with escapes. We study the behavior of the scattering particles in the scattering region, finding an abrupt change of the decay law from algebraic to exponential due to the effects of noise. Moreover, we find a linear scaling law between the coefficient of the exponential law and the intensity of noise. These results are of a general nature in the sense that the same behavior appears when we choose as a model a two-dimensional discrete map with uniform noise (bounded in a particular interval and zero otherwise), showing the validity of the algorithm used. We believe the results of this work be useful for a better understanding of chaotic scattering in more realistic situations, where noise is presented.     

A three-scroll chaotic attractor

This Letter introduces a new chaotic member to the three-dimensional smooth autonomous quadratic system family, which derived from the classical Lorenz system but exhibits a three-scroll chaotic attractor. Interestingly, the two other scrolls are symmetry related with respect to the z-axis as for the Lorenz attractor, but the third scroll of this three-scroll chaotic attractor is around the z-axis. Some basic dynamical properties, such as Lyapunov exponents, fractal dimension, Poincaré map and chaotic dynamical behaviors of the new chaotic system are investigated, either numerically or analytically. The obtained results clearly show this is a new chaotic system and deserves further detailed investigation.     

Projective synchronization of a class of delayed chaotic systems via impulsive control

The Letter studies the projective synchronization of a class of delayed chaotic systems. The drive-response system can be synchronized to within a desired scaling factor via impulsive control. Some sufficient conditions are derived by the stability analysis of the impulsive functional differential equations. An illustrative example is provided to show the effectiveness and feasibility of the proposed method and results.     

Conditions for common-noise-induced synchronization in time-delay systems

We studied synchronization induced by a common external noise in scalar time-delay systems. We have found a set of sufficient conditions for the synchronization. This set of conditions shows that the synchronization occurs in a wide class of time-delay systems. Numerical evidence for the analytically obtained conditions is also presented.     

A special type of attractor and transitions in a delayed system

We discuss strange nonchaotic attractors (SNAs) in addition to chaotic and regular attractors in a quasiperiodically driven system with time delays. A route and the associated mechanism are described for a special type of attractor called strange-nonchaotic-attractor-like (SNA-like) through T² torus bifurcation. The type of attractor can be observed in large parameter domains and it is easily mistaken for a true SNA judging merely from the phase portrait, power spectrum and the largest Lyapunov exponent. SNA-like attractor is not strange and has no phase sensitivity. Conditions for Neimark-Sacker bifurcation are obtained by theoretical analysis for the unforced system. Complicated and interesting dynamical transitions are investigated among the different tongues.     

Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays

In this Letter, we have dealt with the problem of lag synchronization and parameter identification for a class of chaotic neural networks with stochastic perturbation, which involve both the discrete and distributed time-varying delays. By the adaptive feedback technique, several sufficient conditions have been derived to ensure the synchronization of stochastic chaotic neural networks. Moreover, all the connection weight matrices can be estimated while the lag synchronization is achieved in mean square at the same time. The corresponding simulation results are given to show the effectiveness of the proposed method.     

The impulsive control synchronization of the drive-response complex system

This Letter investigates projective synchronization between the drive system and response complex dynamical system. An impulsive control scheme is adapted to synchronize the drive-response dynamical system to a desired scalar factor. By using the stability theory of the impulsive differential equation, the criteria for the projective synchronization are derived. The feasibility of the impulsive control of the projective synchronization is demonstrated in the drive-response dynamical system.     

Multifarious intertwined basin boundaries of strange nonchaotic attractors in a quasiperiodically forced system

A variety of different dynamical regimes involving strange nonchaotic attractors (SNAs) can be observed in a quasiperiodically forced delayed system. We describe some numerical experiments giving evidences of intertwined basin boundaries (smooth, non-Wada fractal and Wada property) for SNAs. In particular, we show that Wada property, fractality and smoothness can be intertwined on arbitrarily fine scales. This suggests that SNAs can exhibit the final state sensitivity and unpredictable behaviors. An interesting dynamical transition of SNAs together with associated mechanisms from non-Wada fractal to Wada intertwined basin boundaries is examined. A scaling exponent is used to characterize the intertwined basin boundaries.