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.
