A New 4D Hyperchaotic System and Its Generalized Function Projective Synchronization

Abstract EN

A new four-dimensional hyperchaotic system is investigated.

Numerical and analytical studies are carried out on its basic dynamical properties, such as equilibrium point, Lyapunov exponents, Poincaré maps, and chaotic dynamical behaviors.

We verify the realizability of the new system via an electronic circuit by using Multisim software.

Furthermore, a generalized function projective synchronization scheme of two different hyperchaotic systems with uncertain parameters is proposed, which includes some existing projective synchronization schemes, such as generalized projection synchronization and function projective synchronization.

Based on the Lyapunov stability theory, a controller with parameters update laws is designed to realize synchronization.

Using this controller, we realize the synchronization between Chen hyperchaotic system and the new system to verify the validity and feasibility of our method.