Analysis of Hopf Bifurcation and Chaos in a Class of Duffing Systems

ABSTRACT This paper focuses on a class of Duffing systems characterized by the presence of a sign function. The study provides a theoretical analysis of the system from a mathematical perspective, categorizing it into three distinct types based on the range of the sign function. Utilizing the KBM method, approximate analytical solutions for these categorized systems are derived. The Hurwitz criterion is employed to conduct a stability analysis of the classified systems, leading to the conclusion that Hopf bifurcation does not occur within the system. Furthermore, through the study of Homoclinic Trajectories, energy curves, and phase diagrams, the system is theoretically analyzed and numerically simulated. The results confirm that the system does not exhibit chaos induced by the cross‐intersection of Homoclinic Trajectories.