Border-collision bifurcation in the Logistic map with state-dependent impulsive forces
Jiang, H; Liu, Y; Zhang, L; et al.Yu, J
Date: 12 April 2024
Article
Journal
Discrete and Continuous Dynamical Systems - Series S
Publisher
American Institute of Mathematical Sciences (AIMS)
Publisher DOI
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 ...
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.
Engineering
Faculty of Environment, Science and Economy
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