A new fractional-order chaotic system with plane equilibrium: Bifurcation analysis, Multi-stability and DSP implementation

Abstract

In this paper, based on the definition of conformable differential, a 4D chaotic system is discretized by Adomian decomposition method (ADM) and its numerical solution is obtained. The stability of the system at the equilibrium point is analyzed. From the coexisting phase diagram, bifurcation model and Lyapunov exponential spectrum, the multi-stability of fractional chaotic systems is analyzed. Spectral entropy complexity is used to study the complex performance of fractional order systems. Then, according to the measurement result of spectrum entropy complexity, three sets of parameters with higher complexity are selected to design a pseudo-random number generator (PRNG). The designed PRNG passed all randomness tests, indicating that the system has high practical application value. Meanwhile, the related design of the circuit implementation of the chaotic system was completed and verified on the DSP platform. Research shows that fractional-order chaotic systems have special dynamic behaviors and multiple stability phenomena that evolve with q. The pseudo-random sequence generator and digital circuit designed in this research provide guidance for the application of fractional-order chaotic systems.