Bifurcations of planar Hamiltonian systems with impulsive perturbation
Zhaoping Hu, Maoan Han, Valery G. Romanovski
TL;DR
This paper investigates how impulsive perturbations affect the bifurcation of harmonic and subharmonic solutions in planar Hamiltonian systems, providing conditions for their existence using Melnikov functions.
Contribution
It introduces new sufficient conditions for the existence of harmonic and subharmonic solutions in impulsively perturbed Hamiltonian systems using Melnikov functions.
Findings
Established conditions for bifurcation of solutions
Demonstrated existence of harmonic solutions
Analyzed subharmonic bifurcations
Abstract
In this paper, by means of the Melnikov functions we consider bifurcations of harmonic or subharmonic solutions from a periodic solution of a planar Hamiltonian system under impulsive perturbation. We give some sufficient conditions under which a harmonic or subharmonic solution exists.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Quantum chaos and dynamical systems · Mathematical and Theoretical Epidemiology and Ecology Models