Complex Dynamics and Sliding Bifurcations of the Filippov Lorenz–Chen System

Abstract

In this paper, we propose a Filippov switching model which is composed of the Lorenz and Chen systems. By employing the qualitative analysis techniques of nonsmooth dynamical systems, we show that the new Filippov system not only inherits the properties of the Lorenz and Chen systems but also presents new dynamics including new chaotic attractors such as four-wing butterfly attractor, Lorenz attractor with sliding segments, etc. In particular, we find that different new attractors can coexist such as the coexistence of two-point attractors and chaotic attractor, the coexistence of two-point attractors and quasi-periodic solution, the coexistence of transient transition chaos and quasi-periodic solution. Furthermore, nonsmooth bifurcations and numerical analyses reveal that the proposed Filippov system has a series of new sliding bifurcations including a symmetric pair of sliding mode bifurcations, a symmetric pair of sliding Hopf bifurcations, and a symmetric pair of Hopf-like boundary equilibrium bifurcations.