Dynamics Analysis and Circuit Simulation of A New Chaotic System with A Compound Power Function and Coexisting Attractors

doi:10.19596/j.cnki.1001-246x.8335

Abstract

Abstract:

A new three-dimensional continuous autonomous chaotic system with a compound power function is constructed. The equation of state of the system has only five terms, one of which is a compound power function with an exponent less than 1. The system has properties of simple structure, non-hyperbolic equilibrium point, coexistence of attractors, and exhibits complex dynamic behaviors. Firstly, dynamic behaviors including Lyapunov exponential spectrum, bifurcation diagram and Poincaré mapping are analyzed. It shows that the system has chaotic characteristics. Then, circuit design of the chaotic system is carried out. Circuit simulation results verify the theoretical analysis.

Key words: chaotic system, compound power function, coexisting attractor, dynamics analysis, circuit simulation

CLC Number:

TP391

Qicheng XU, Changchun SUN. Dynamics Analysis and Circuit Simulation of A New Chaotic System with A Compound Power Function and Coexisting Attractors[J]. Chinese Journal of Computational Physics, 2021, 38(6): 742-748.

Figures/Tables 10

Fig.1 A chaotic attractor (a) x - y plane; (b) x - z plane; (c) y - z plane; (d) three-dimensional phase diagram

Fig.2 Lyapunov exponents

Fig.3 Bifurcation diagram

Fig.4 Poincaré mapping

Fig.5 A periodic attractor

Fig.6 Coexisting attractors

Fig.7 Simulation circuit diagram

Fig.8 Compound power function simulation circuit diagram

Fig.9 Projections of the chaotic attractor in phase planes (a) x - y plane; (b) x - z plane; (c) y - z plane

Fig.10 Time domain waveforms (a) x - t waveform; (b) y - t waveform; (c) z - t waveform

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