Robust Synchronization of Hyperchaotic Systems with Uncertainties and External Disturbances

Abstract

The robust synchronization of hyperchaotic systems with uncertainties and external disturbances is investigated. Based on the Lyapunov stability theory, the appropriate adaptive controllers and parameter update laws are designed to achieve the synchronization of uncertain hyperchaotic systems. The robust synchronization of two hyperchaotic Chen systems is taken as an example to verify the feasibility of the presented schemes. The size of the subcontroller gain’s influences on the convergence speed is discussed. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed synchronization schemes.

Globally exponential synchronization criterion of chaot-ic oscillators using active control

“…the linear feedback gains of the controllers are selected as . In numerical simulation, the following unknown external disturbances are applied to the master and slave systems (20) respectively. (20), the time histories of the convergence of the error states are displayed in Figure 3.…”

“…Assumption 2.1: It is assumed that the unknown external disturbances ( ) and ( ) are the norm-bounded in [20]. i.e.…”

“…The complete synchronization is then described as follows: (20) with identical parameters , and in spite of the dissimilarities in their initial conditions. For the complete synchronization (20), the synchronization error systems is described as follows: (20) is designed such that the following inequality holds true:…”

“…where ( ) and ( ) , represent the minimum and maximum eigenvalues of two positive definite matrices (PDM) and , respectively then, the two identical BVP chaotic oscillators (20) are globally exponentially synchronized.…”

Single input sliding mode control for hyperchaotic Lu system with parameter uncertainty

“…These chaotic and/or hyperchaotic systems show different dynamical properties. So far, various types of synchronization phenomenon have been found such as functional synchronization [2], complete synchronization [3], observer based synchronization [4], phase synchronization [5], generalized synchronization [6], anti-synchronization [7][8][9], distributed synchronization [10], robust synchronization [11], and projective synchronization [12,13]. Transition of synchronization [14][15][16][17][18] induced in the chaotic systems has been explored extensively.…”