Periodic Solutions and Stability Analysis for Two-Coupled-Oscillator Structure in Optics of Chiral Molecules

Abstract

Chirality is an indispensable geometric property in the world that has become invariably interlocked with life. The main goal of this paper is to study the nonlinear dynamic behavior and periodic vibration characteristic of a two-coupled-oscillator model in the optics of chiral molecules. We systematically discuss the stability and local dynamic behavior of the system with two pairs of identical conjugate complex eigenvalues. In particular, the existence and number of periodic solutions are investigated by establishing the curvilinear coordinate and constructing a Poincaré map to improve the Melnikov function. Then, we verify the accuracy of the theoretical analysis by numerical simulations, and take a comprehensive look at the nonlinear response of multiple periodic motion under certain conditions. The results might be of important significance for the vibration control, safety stability and design optimization for chiral molecules.