A 3D chaotic system with piece-wise lines shape non-hyperbolic equilibria and its predefined-time control

Abstract

Abstract In this paper, a novel 3D chaotic system with an infinite number of equilibria is proposed and its predefined-time control is studied. The system has non-hyperbolic equilibria with piece-wise shape, which is special and rarely mentioned before. Through 0-1 test, Lyapunov exponent, bifurcation diagram and complexity analysis, the system is deeply investigated. A reverse bubble (Feigenbaum remerging tree) is found in the system, which proves the anti-monotonicity. Furthermore, the circuit of the system is designed and the real experiment is carried out to verify its dynamic characteristics. Finally, according to the theory of predefined-time stability, a predefined time controller is designed for the system. By adding only one controller to the system, the objective of stabilizing the system within a predefined time can be achieved successfully, and simulation analysis shows good performance of the controller.