This paper presents a four-dimension hyperchaotic Lorenz system, obtained by adding a nonlinear controller to Lorenz chaotic system. The hyperchaotic Lorenz system is studied by bifurcation diagram, Lyapunov exponents spectrum and phase diagram. Numerical simulations show that the new system’s behavior can be convergent, divergent, periodic, chaotic and hyperchaotic when the parameter varies.

A hyperchaos generated from Lorenz system

This paper studies the adaptive complete synchronization of chaotic and hyperchaotic systems with fully unknown parameters. In practical situations, some systems’ parameters cannot be exactly known a priori, and the uncertainties often affect the stability of the process of synchronization of the chaotic oscillators. An adaptive scheme is proposed to compensate for the effects of parameters' uncertainty based on the structure of chaotic systems in this paper. Based on the Lyapunov stability theorem, an adaptive controller and a parameters update law can be designed for the synchronization of chaotic and hyperchaotic systems. The drive and response systems can be nonidentical, even with different order. Three illustrative examples are given to demonstrate the validity of this technique, and numerical simulations are also given to show the effectiveness of the proposed chaos synchronization method. In addition, this synchronization scheme is quite robust against the effect of noise.

Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters.

In this paper, the adaptive synchronization and lag synchronization are considered for uncertain dynamical system with time delay based on parameter identification and a novel control method is then further given using the Lyapunov functional method. With this new and effective method, parameter identification and lag synchronization can be achieved simultaneously. Simulation results are given to justify the theoretical analysis in this paper.

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Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification

Through the construction of a suitable fitness function, the problem of parameters estimation of the chaotic system is converted to that of parameters optimization. In this paper, an optimization method, called CAS (chaotic ant swarm), is developed to solve the problem of searching for the optimal. Finally numerical simulations are provided to show the effectiveness and feasibility of the developed method.

Parameters identification of chaotic systems via chaotic ant swarm

This first technical session is further developing the technological dimensions of technology transfer, with three illustrations of successful and representative industrial applications. It covers the cases of embedded autonomy in spacecraft applications, advanced avionics solutions for satellite communication and component hybridization for navigation.

Ja Hu

Papers

Adaptive synchronization of uncertain Rossler hyperchaotic system based on parameter identification