Quasi-synchronization dynamics of coupled and driven plasma oscillators

Abstract

The dynamics of two coupled and periodically driven plasma oscillators is investigated in this paper. It is shown that the two oscillators exhibit rich dynamical transition to a quasi-synchronized state. Stability and sufficient criteria for synchronization are analytically obtained using linear matrix inequality (LMI) and the Routh–Hurwitz criterion; and qualitatively characterized by the system’s interaction energies. Moreover, the transition dynamics is rich with abundant complex bifurcation structures, including Hopf bifurcations. Based on the method of multiple time-scale, steady state equations for the vibration of the coupled oscillators have also been obtained, and bi-resonance induced by coupling at distinct frequencies are reported.