Stabilization of a Four-Dimensional Chaotic System with No Equilibria via a Novel Precise Constant-Control Approach

A problem on stabilization of a four-dimensional chaotic system is investigated. A novel precise constant-control approach is derived in this paper. A four-dimensional chaotic system with five parameters and eight terms is constructed firstly. The polynomial chaotic system is composed of four linear terms, one constant term and three quadratic nonlinear terms. The system has no any equilibrium point. A new hidden attractor can be generated from the four-dimensional polynomial system. Bifurcation diagrams of four state variables with the variation of a single parameter are depicted respectively. A novel precise constant-control approach is designed to stabilize the chaotic system. Corresponding numerical simulations verify the effectiveness of the novel approach derived in this paper.