Dynamics of a class of non-smooth Lorenz systems in the sense of Filippov

There are many phenomena in weather and climate systems that can be represented by non-smooth systems. The non-smooth extension of the classical smooth Lorenz system is a typical and simplified model, which can be used to describe the strange dynamics in weather and climate systems. The dynamics of a class of non-smooth Lorenz systems are studied in this article. This system is a Filippov switching model, which is composed of two smooth Lorenz systems with different parameters. The non-smooth system can be thought of as the symmetric breaking of the original smooth system, which can generate new dynamical behavior. The local analysis of the sliding dynamics is provided. A geometric model is introduced and the mechanism underlying the existence of the chaotic dynamics is explained. Some numerical calculations illustrate the existence of strange attractors with infinite sliding, the bifurcation of switching manifolds leading to the existence of strange attractors, and the complicated geometric structure of the attractors, different from the well-known Lorenz attractor in the classical smooth Lorenz system.