Border-collision bifurcation in the Logistic map with state-dependent impulsive forces

Abstract

This paper examines the intricate dynamics of the Logistic map involving impulsive forces that depend on the state. The conditions of stability and border-collision bifurcation (BCB) of periodic orbits are presented. The two-parameter dynamical regions and the two-parameter bifurcation diagram of the system with respect to the system parameter and the strength of impulsive force are constructed. The periodic tongues are given to show that the BCB is critical for the dynamics of the Logistic map with state-dependent impulsive forces. Finally, the bifurcation curves are provided to disclose the mechanisms of several bifurcation scenarios closely related to the BCB, including the period increment scenario and the period-adding scenario.