Quasi-synchronization dynamics of coupled and driven plasma oscillators

• Two coupled and driven plasma oscillators are shown to exhibit quasi-synchronization.
• The preceding dynamics to quasi-synchronization is characterized by complex dynamics.
• LMI was used to examine the criteria and threshold for quasi-synchronization.
• Steady state equations for the system was obtained using multiple time-scale method.
• Coupling is shown to induce bi-resonances at distinct frequencies.

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 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.