Sliding homoclinic orbits and chaotic dynamics in a class of 3D piecewise-linear Filippov systems

In this paper, sliding homoclinic orbits are demonstrated as a source of chaotic dynamics in a class of three-dimensional Filippov systems. Such orbits are composed of three parts: (i) an arc of sliding motion; (ii) a stable manifold connecting the origin and switching manifold; (iii) an unstable manifold connecting the origin and switching manifold. After establishing certain hypothetical conditions, we propose analytical criteria for the coexistence of two sliding homoclinic orbits. The dynamic behaviors near homoclinic orbits are revealed by analyzing the properties of Poincaré return maps. It is found that trajectories close to sliding homoclinic orbits are particularly sensitive to the initial conditions. Additionally, we investigate the existence of multistability generated by initial conditions perturbations and the process of chaotic evolutions via parameter variations. Numerical simulations show that the type of sliding attractors will be significantly affected by a modest change in the parameter values. To the best of our knowledge, there are few articles highlighting the unique characteristics of three-dimensional Filippov systems with two switching manifolds.