Bifurcation Analysis and Chaos Suppression in Autonomous Continuous-Time Systems with Saturation Nonlinearity Using Nonlinear State Feedback

This paper investigates the dynamic behavior and control of autonomous continuous-time nonlinear systems exhibiting saturation nonlinearity. A detailed bifurcation analysis is conducted to understand how system parameters influence the onset of complex dynamics, including periodic oscillations and chaos. To suppress undesired chaotic behavior, a nonlinear state feedback control strategy is proposed, leveraging saturation characteristics for practical actuator constraints. Theoretical analysis guarantees convergence and stability of the closed-loop system. Numerical simulations on representative nonlinear models illustrate the effectiveness of the proposed control method in eliminating chaos and achieving desired system performance. Finally, potential applications and extensions to higher-dimensional systems are discussed.