Extreme Multi-stability of a Four-dimensional Chaotic System with Infinitely Many Symmetric Homogeneous Attractors

Abstract

A new four-dimensional chaotic system with extreme multi-stability based on a classic three-dimensional chaotic system is proposed. The new system has a line equilibrium point, which can generate an infinite number of symmetrical homogeneous attractors. The chaotic characteristics of the system are analyzed by phase orbit diagram and Poincare section methods. Using phase orbit diagrams, bifurcation diagrams and Lyapunov exponent spectrum methods, the influence of initial conditions on the extreme multi-stability of the system is analyzed. The analysis shows that the system has a large initial value variation range, and the Lyapunov exponent spectrum is constant except for the zero point. In addition, the system also has centrally symmetrical discrete bifurcation diagrams. Furthermore, we studied the relationship between the initial symmetry of the system and the symmetry of the attractor, which is different from the symmetrical attractor in the existing chaotic system, which can generate an infinite number of symmetrical homogeneous attractors. Finally, circuit simulation software is used to build an analog circuit to capture the chaotic attractor of the system, and the result verifies the correctness of the numerical simulation.