Chaos in a Simple Saturation System

Systems with saturation nonlinearities are frequently encountered in engineering problems. In this paper, the dynamics of the three-dimensional saturated system [Formula: see text] is studied. We find rich dynamics in this system through numerical simulations, including chaotic attractors and transient chaos. We conduct both theoretical analysis and numerical analysis of this system. Numerical results suggest that there may exist a heteroclinic network among periodic orbits, which gives rise to chaos. Furthermore, based on the theory of topological horseshoes and by numerical methods, we find that for certain parameters there exist topological horseshoes under the fourth Poincaré return map in this system, thereby demonstrating the existence of chaos. Our study reveals that a simple saturation system can exhibit chaos, deepening our understanding of the influence of saturation on system dynamics.