Adomian Decomposition, Dynamic Analysis and Circuit Implementation of a 5D Fractional-Order Hyperchaotic System

Abstract

In this paper, a class of fractional-order symmetric hyperchaotic systems is studied based on the Adomian decomposition method. Starting from the definition of Adomian, the nonlinear term of a fractional-order five-dimensional chaotic system is decomposed. At the same time, the dynamic behavior of a fractional-order hyperchaotic system is analyzed by using bifurcation diagrams, Lyapunov exponent spectrum, complexity and attractor phase diagrams. The simulation results show that with the decrease of fractional order q, the complexity of the hyperchaotic system increases. Finally, based on the fractional-order circuit design principle, a circuit diagram of the system is designed, and the circuit is simulated by Multisim. The results are consistent with the numerical simulation results, which show that the system can be realized, which provides a foundation for the engineering applications of fractional-order hyperchaotic systems.

Keywords

• Adomian decomposition
• fractional-order chaotic system
• Lyapunov exponent spectrum
• circuit design