Dynamic behaviors of a star-coupled underdamped system with multiplicative quadratic noise and periodic excitation

Abstract

The star-coupled linear underdamped system subject to multiplicative quadratic noise and periodic sinusoidal excitation are considered. The multiplicative noise is modeled as a quadratic polynomial function of symmetric trichotomous noise. Firstly, the stability conditions of the system and the stationary solution of the mean field are deduced by establishing the differential equations of the mean field. Then the synchronization conditions of the principal and general particles are obtained respectively. These conditions are beneficial for studying the collective behavior of the system and the motion characteristics of particles in different situations. Then the output signal-to-noise ratio of the coupled system is derived in detail for the first time. Moreover, the dynamic behaviors of the system are analyzed by analytical results and numerical simulations, including the collective behavior under different conditions, and the concrete influence of parameters on the output signal-to-noise ratio.