Free Control Based on Chaotic Systems Without Equilibrium

Abstract Chaotic system without equilibrium is a hot topic in recent years, and its unique dynamic characteristics have caused extensive research. In this paper, different chaotic systems without equilibrium are obtained by modifying the Sprott-A system equations. The test results show the first new system is conservative. After investigating the hidden dynamical behavior of the first system, the rotation attractor phenomenon was observed by the rotation factor. Next, we make a second transformation of the Sprott-A system. By introducing trigonometric function, we can get a new system that can generate infinite coexisting grid attractors. After calculation, we find that the new system still belongs to the chaotic system without equilibrium point. It is different from chaotic system with equilibrium point, which depends on the movement of equilibrium point to produce attractor coexistence. The new system proposed in this paper has no equilibrium points, and the coexistence attractor phenomenon can be observed only by changing initial values. The chaotic system without equilibrium point which can realize the coexistence of attractors provides potential application value for some related fields, it is worthy of further study.