Generalized Function Projective Synchronization of Two Different Chaotic Systems with Uncertain Parameters

This study proposes a new approach to realize generalized function projective synchronization (GFPS) between two different chaotic systems with uncertain parameters. The GFPS condition is derived by converting the differential equations describing the synchronization error systems into a series of Volterra integral equations on the basis of the Laplace transform method and convolution theorem, which are solved by applying the successive approximation method in the theory of integral equations. Compared with the results obtained by constructing Lyapunov functions or calculating the conditional Lyapunov exponents, the uncertain parameters and the scaling function factors considered in this paper have fewer restrictions, and the parameter update laws designed for the estimation of the uncertain parameters are simpler and easier to realize physically.

Automated summary

This study presents a new method to achieve generalized function projective synchronization (GFPS) between two different chaotic systems with uncertain parameters. By converting the differential equations of the synchronization error systems into Volterra integral equations through Laplace transform and convolution theorem, the GFPS condition is derived. The approach utilizes the successive approximation method to solve the integral equations. Compared to other methods, the proposed approach has fewer restrictions on uncertain parameters and simpler physically realizable parameter update laws.