Asymptotic stability and bifurcations of a perturbed McMillan map

Abstract

Abstract This paper presents various bifurcations of the McMillan map under perturbations of its coefficients, such as period-doubling, pitchfork, and hysteresis bifurcation. The associated existence regions are located. Using the quasi-Lyapunov function method, the existence of asymptotically stable fixed point is also demonstrated.

Keywords

• McMillan map
• Period-doubling bifurcation
• Pitchfork bifurcation
• Hysteresis bifurcation
• Asymptotic stability