The Existence and Upper Bound of Periodic Solutions for Two-Coupled-Oscillator Model in Optics Chiral Molecular Medium

Abstract

Abstract In this paper, we focus on the two-coupled-oscillator model in optics chiral molecular medium. We perform scale transformations for variables and study the existence of periodic solutions in detail for the two-coupled-oscillator system. We obtain the Melnikov function by establishing the curvilinear coordinate transformation and constructing a Poincaré map. Then the existence of periodic solutions of this oscillator system is analyzed when unperturbed system is Hamiltonian system. We apply them to discuss the upper bound of periodic solutions of this oscillator system and give the configuration of the phase diagram by numerical simulation. It has great theoretical significance to study the non-planar motion of the two-coupled-oscillator system for analyzing dynamic characteristics in optics chiral molecular medium.