The Comparison, Analysis and Circuit Implementation of the Chaotic Systems

Abstract

A four-dimensional chaotic system with complex dynamical properties is constructed. The complexity of the system was evaluated by equilibrium point, Lyapunov exponential spectrum and bifurcation model. The coexistence of Lyapunov exponential spectrum and bifurcation model proves the coexistence of attractors. [Formula: see text] and SE complexity algorithms are used to compare and analyze the corresponding complexity characteristics of the system, and the most complex integer-order system is obtained. In addition, the circuit to switch between different chaotic attractors is novel. In particular, more complex parameters are selected for the fractional-order chaotic system through the analysis of parameter complexity, and the rich dynamics of the system are analyzed. Experimental results based on Field-Programmable Gate Array (FPGA) platform verify the feasibility of the system. Finally, the most complex integer-order system is compared with its corresponding fractional-order system in image encryption, so that the fractional-order system has a better application prospect.