Synchronization between Two Different Hyperchaotic Systems Containing Nonlinear Inputs
This paper introduces a variable structure technology for the synchronization of chaos between two different hyperchaotic systems with input nonlinearity. Based on Lyapunov stability theory, a sliding mode controller and some generic sufficient conditions
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Department of Electrical Engineering, Far-East University, Tainan 744, Taiwan, R.O.C. [email protected] 2 Department of Mechanical Engineering, Far-East University, Tainan 744, Taiwan, R.O.C. [email protected]
Abstract. This paper introduces a variable structure technology for the synchronization of chaos between two different hyperchaotic systems with input nonlinearity. Based on Lyapunov stability theory, a sliding mode controller and some generic sufficient conditions for global asymptotic synchronization are designed such that the error dynamics of the hyperchaotic Rössler and hyperchaotic Chen systems satisfy stability in the Lyapunov sense in spit of the input nonlinearity. The Numerical simulation results demonstrate the validity and feasibility of the proposed controller.
1 Introduction Since the ideal of synchronizing two identical chaotic systems from different initial conditions was first introduced by Carroll and Pecora, chaos synchronization has gained a lot of attention among scientists from variety of research fields over the last few years [1-3]. Chaos synchronization can be applied in the vast areas of physics and engineering science, especially in secure communication [4-5]. In order to achieve the synchronization, a nonlinear controller that obtains signals from the master and slave systems and manipulates the slave system should be designed. Recently, many control methods have been developed to achieve chaos synchronization between two identical chaotic systems with different initial conditions [6-11]. However, most of these methods are only applicable to the chaos synchronization of two systems that are identical in every respect and which contain only low dimensional attractors. This is in stark contrast to many real-word applications of the technology. In fact, in systems such as laser array, biological systems and cognitive processes, it is hardly the case that every component can be assumed to be identical. In the area of communications security for example, the adoption of higher dimensional chaotic systems as well as systems with more than one positive Lyapunov exponents has been proposed for use to generate more complex dynamics. Methods are therefore needed to synchronize chaotic systems that are both different and are of high dimensions. Moreover, when the controller is realized in practical physical systems, due to physical limitations of actuators, the nonlinearities in control input do exist. The presence of nonlinearities in control input may cause serious influence of system performance and decrease the system response. Besides, the nonlinearity in control input may cause the chaotic system J.-W. Park, T.-G. Kim, and Y.-B. Kim (Eds.): AsiaSim 2007, CCIS 5, pp. 133–141, 2007. © Springer-Verlag Berlin Heidelberg 2007
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H.-T. Yau, C.-C. Wang, and M.-L. Hung
perturbed to unpredictable results because the chaotic system is very sensitive to any system parameters. Therefore, its effect cannot be ignored in analysis of control design and realization for chaos synchronizat
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