Discrete Chaotic Systems Research Articles

Lag synchronization between discrete chaotic systems with diverse structure

A lag synchronization controller is designed in studying discrete chaotic systems with diverse structures to realize synchronization between Henon and Ikeda systems. The structure of the lag synchronization controller and the error equations of state variables between discrete chaotic systems are presented based on the stability theory. The designed controller has unique structures for different chaotic systems. Lag synchronization between any discrete chaotic systems with diverse structures can be achieved. Simulation results show that this control method is effective and feasible.

Adaptive Function Projective Synchronization of Discrete Chaotic Systems with Unknown Parameters

Adaptive function projective synchronization of discrete-time chaotic systems with unknown parameters is considered. Based on the contraction mapping theorem, proper controllers and estimators are designed. Illustrative examples are provided to show the effectiveness of this method.

Improved piece-wise linear and nonlinear synchronization of a class of discrete chaotic systems

This paper deals with the chaotic synchronization of a discrete chaotic system. Based on a stable analysis, improved piece-wise linear feedback and nonlinear feedback control methods were given. Both the methods can achieve chaotic synchronization efficiently with one control input. The range of coupling coefficient is calculated in both the methods. Compared with nonlinear controls, the improved piece-wise linear controls have simpler structures and can be obtained more easily. Finally, the numerical simulation results verified the effectiveness of both the methods.

How to make dull cellular automata complex by adding memory: Rule 126 case study

AbstractUsing Rule 126 elementary cellular automaton (ECA), we demonstrate that a chaotic discrete system — when enriched with memory — hence exhibits complex dynamics where such space exploits on an ample universe of periodic patterns induced from original information of the ahistorical system. First, we analyze classic ECA Rule 126 to identify basic characteristics with mean field theory, basins, and de Bruijn diagrams. To derive this complex dynamics, we use a kind of memory on Rule 126; from here interactions between gliders are studied for detecting stationary patterns, glider guns, and simulating specific simple computable functions produced by glider collisions. © 2010 Wiley Periodicals, Inc. Complexity, 2010

Chaotic synchronization using PID control combined with population based incremental learning algorithm

Evolutionary algorithms (EAs) refer to a broad class of optimization algorithms, which take some inspiration from evolutionary systems in the natural world. In recent years, a new class of EAs called estimation of distribution algorithms (EDAs) has emerged based on probabilistic modeling of the search space. Instances of EDAs include population based incremental learning (PBIL) algorithm. The PBIL algorithm is an easy to understand heuristic optimization technique that is inspired by the genetic algorithm and the competitive learning paradigm. PBIL includes many of the features from the genetic algorithm such as binary string representation, the notion of individuals, fitness measures and mutations. Contrary to the genetic algorithm it does not maintain a population of individuals but instead PBIL contains a probability vector. At each generation a new population of individuals is sampled according to the probabilities specified in the probability vector. The population is evaluated and the probability vector is updated by dragging it towards the best individual in the population. In recent years, the investigation of synchronization of chaotic systems has attracted much attention of researchers. Chaos synchronization has been applied in many fields such as secure communication, chemical, engineering, and biological systems, among others. This paper presents the synchronization of two identical discrete chaotic systems subject the different initial conditions by designing a proportional–integral–derivative (PID) controller. In addition, the tuning of the PID controller based on a modified PBIL algorithm using similarity analysis is also investigated in this paper. Simulation results show the good performance of the modified PBIL algorithm for synchronization of chaotic systems.

利用主动-被动法实现Bragg声光双稳系统的混沌同步

An active-passive method is used in discrete chaotic systems to study chaos synchronization.A discrete system is generally divided based on Lyapunov stability theory,and synchronization of discrete chaotic systems is realized.Bragg acousto–optic bistable system is taken as an example to verify the effectiveness of the method.Simulation results show that the error variable of two Bragg acousto–optic bistable systems with different initials approach zero smoothly and rapidly in a short series of time,which shows the method is effective and practical.The method is proper to any discrete or continuous chaotic systems with different initials,and it can be generally used.

Hybrid Lag Function Projective Synchronization of Discrete Chaotic Systems with Different Orders

This paper presents a novel method to achieve hybrid lag function projective synchronization between two different discrete chaotic systems with different orders, which (is a further development of generalized function projective synchronization. On the basis of Lyapunov' stability theory, a controller is designed to guarantee synchronization of drive and response systems. Numerical simulations are provided to verify the proposed synchronization approach.

A modified ant colony optimization algorithm based on differential evolution for chaotic synchronization

Optimization algorithms inspired by the ants’ foraging behavior have been initially used for solving combinatorial optimization problems. Since the emergence of ant algorithms as an optimization tool, some attempts were also made to use them for tackling continuous optimization problems. In recent years, the investigation of synchronization and control problem for discrete chaotic systems has attracted much attention, and many possible applications. The optimization of a proportional–integral–derivative (PID) controller based on a modified continuous approach of ant colony optimization combined with a differential evolution method (MACO) for synchronization of two identical discrete chaotic systems subject the different initial conditions is presented in this paper. Numerical simulations based on optimized PID control of a nonlinear chaotic model demonstrate the effectiveness and efficiency of MACO approach. Simulation results of the MACO to determine the PID parameters are compared with other metaheuristics including a classical ant colony optimization approach, genetic algorithm and evolution strategy. The proposed approach of PID tuning based on MACO can be generalized to other chaotic systems.

Analysis of random-like property of discrete chaotic system with symbol entropy

Random-like properties of typical Logistic map and Henon map were analyzed and discussed by using symbol entropy algorithm.Firstly,the binary sequences were obtained from real-valued sequences generated by discrete chaotic maTP,then were coded.Symbol entropies of the binary sequences were calculated and their curves were plotted.Influences of system parameter and initial value on symbol entropy were discussed.Simulation results show that symbol entropy algorithm can be used to statistically identify the strength of random-like properties of discrete chaotic maTP,and Logistic map is better than Henon map as the source of randomness.

Stabilizability of discrete chaotic systems via unified impulsive control

This Letter is concerned with the asymptotical stabilization problem of discrete chaotic systems by using a novel unified impulsive control scheme. Sufficient conditions for asymptotical stability of the impulsive controlled discrete systems are obtained by means of the Lyapunov stability theory and algebraic inequality techniques. Finally, numerical simulations on the Hénon and Ushio discrete chaotic systems are presented to illustrate the effectiveness and usefulness of the unified impulsive control scheme.

Implementation of dynamic programming for chaos control in discrete systems

In this paper the control of discrete chaotic systems by designing linear feedback controllers is presented. The linear feedback control problem for nonlinear systems has been formulated under the viewpoint of dynamic programming. For suppressing chaos with minimum control effort, the system is stabilized on its first order unstable fixed point (UFP). The presented method also could be employed to make any desired n th order fixed point of the system, stable. Two different methods for higher order UFPs stabilization are suggested. Afterwards, these methods are applied to two well-known chaotic discrete systems: the Logistic and the Henon Maps. For each of them, the first and second UFPs in their chaotic regions are stabilized and simulation results are provided for the demonstration of performance.

Image encryption based on chaotic system with variable parameters

Concerning the degeneracy of the computer limited precision effect in a single one-dimensional discrete chaotic system,this article proposed a method of pseudo-random sequence generation with variable parameters in the process of the generation of the chaotic signal.The constructed chaos system based on this method had some advantages,such as the long cycle of pseudo-random sequence,the large quantity of key and the big superiority of key space,and the prodeced password has a higher safety performance.Besides,based on the method,a new image encryption algorithm was put forward.The simulation results show that this algorithm is simple,safe and easy to meet the software and hardware requirements.

Reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems

The problem of reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems is investigated in this paper. Firstly a reliable impulsive controller is designed by the impulsive control theory. Then, some sufficient conditions for reliable impulsive lag synchronization between the drive system and the response system are obtained. Numerical simulations are given to show the effectiveness of the proposed method.

PID control design for chaotic synchronization using a tribes optimization approach

Recently, the investigation of synchronization and control problems for discrete chaotic systems has stimulated a wide range of research activity including both theoretical studies and practical applications. This paper deals with the tuning of a proportional-integral-derivative (PID) controller using a modified Tribes optimization algorithm based on truncated chaotic Zaslavskii map (MTribes) for synchronization of two identical discrete chaotic systems subject the different initial conditions. The Tribes algorithm is inspired by the social behavior of bird flocking and is also an optimization adaptive procedure that does not require sociometric or swarm size parameter tuning. Numerical simulations are given to show the effectiveness of the proposed synchronization method. In addition, some comparisons of the MTribes optimization algorithm with other continuous optimization methods, including classical Tribes algorithm and particle swarm optimization approaches, are presented.

Influence of noise on the sample entropy algorithm

We study the effect of static additive noise on the sample entropy (SampEn) algorithm [J. S. Richman and J. R. Moorman, Am. J. Physiol. Heart Circ. Physiol. 278, 2039 (2000); R. B. Govindan et al., Physica A 376, 158 (2007)] for analyzing time series. Using surrogate data tests, we empirically investigate the ability of the SampEn index to detect nonlinearity in simulated time series corrupted by increased amounts of noise. Discrete and continuous chaotic and nonchaotic systems are included in the numerical experiments. Both Gaussian and uniformly distributed noises are considered. The results indicate that the SampEn statistic is a robust index for detecting nonlinearity in time series corrupted by observational noise.

A NEW DELAYED FEEDBACK CONTROL SCHEME FOR DISCRETE TIME CHAOTIC SYSTEMS

In this paper we consider the stabilization problem of unstable periodic orbits of discrete time chaotic systems. We consider both one dimensional and higher dimensional cases. We propose a novel generalization of the classical delayed feedback law and present some stability results. These results show that for period 1 all hyperbolic periodic orbits can be stabilized with the proposed method. Although for higher order periods the proposed scheme may possess some limitations, some improvement over the classical delayed feedback scheme still can be achieved with the proposed scheme. The stability proofs also give the possible feedback gains which achieve stabilization. We will also present some simulation results.

A NEW GENERALIZATION OF DELAYED FEEDBACK CONTROL

In this paper, we consider the stabilization problem of unstable periodic orbits of one-dimensional discrete time chaotic systems. We propose a novel generalization of the classical delayed feedback law and present some stability results. These results show that for period 1 all hyperbolic periodic orbits can be stabilized by the proposed method; for higher order periods the proposed scheme possesses some inherent limitations. However, some more improvement over the classical delayed feedback scheme can be achieved with the proposed scheme. The stability proofs also give the possible feedback gains which achieve stabilization. We will also present some simulation results.

Integral Particle Swarm Optimization with Dispersed Accelerator Information

Integral-controlled particle swarm optimization (ICPSO) is an effective variant of particle swarm optimization (PSO) aiming to increase the population diversity. Due to the additional accelerator items, the behavior of ICPSO is more complex, and provides more chances to escaping from a local optimum than the standard version of PSO. However, many experimental results show the performance of ICPSO is not always well because of the particles' un-controlled movements. Therefore, a new variant, integral particle swarm optimization with dispersed accelerator information (IPSO-DAI) is designed to improve the computational efficiency. In IPSO-DAI, a predefined predicted velocity index is introduced to guide the moving direction. If the average velocity of one particle is superior to the index value, it will choice a convergent manner, otherwise, a divergent manner is employed. Furthermore, the choice of convergent manner or divergent manner for each particle is associated with its performance to fit different living experiences. Simulation results show the proposed variant is more effective than other three variants of particle swarm optimization especially for multi-modal numerical problems. The IPSO-DAI algorithm is also applied to directing the orbits of discrete chaotic dynamical systems by adding small bounded perturbations, and achieves the best performance among four different variants of PSO.

Chaotic digital communication system based on field programmable gate array technology—Design and implementation

A novel universal approach for design and implementation of chaotic digital communication system based on IEEE-754 standard and field programmable gate array technology (FPGA) is proposed, combing chaos encryption with traditional cipher realization. By using the Euler algorithm and appropriate discrete processing, the continuous chaotic system is converted to a discrete chaotic system. Using FPGA hardware design system, digital chaotic sequence is generated as the key. Scrambling and expansion encryption algorithm is realized and analyzed. Driven and response of secure communication system is designed by constructing a loop including the signal and achieving chaotic synchronization between sender and receiver. Taking grid Chua chaotic system as an example, the secure communication system using FPGA hardware platform is implemented. The technical development process, algorithm flow chart, hardware design and realization result are also given.

LoBa128, a Lorenz-based PRNG for wireless sensor networks

In this paper we focus on the development of a pseudo-random number generator (PRNG) to be used as a key generator for a symmetrical encryption system in a one-time-pad like environment, particularly useful for WSN. Our PRNG is based on the Lorenz chaotic system through a new approach of applicability of chaotic systems to cryptography, that we named 'modular-chaos'. We evaluate our proposal using both analytical and experimental techniques that lead us to an efficient and robust solution against statistical attacks and present strong random properties. Our approach solves the problem of short-cycle length of discrete chaotic systems.