Numerical study on synchronization in the Rayleigh-Duffing and Duffing oscillators

A study on the master-slave synchronization scheme between Rayleigh-Duffing and Duffing oscillators is presented. We analyze the elastic and dissipative couplings and a combination of both. We compare the results to explore which coupling is more effective to achieve synchronization between both oscillators. The numerical results demonstrate that for the elastic or dissipative coupling at best there is complete synchronization in only one state of the slave system. However, it was also observed that depending on which oscillator acts as the master system and the coupling used, there may be partial or complete synchronization for large values of the coupling strength. When the combination of both couplings is used, there always exists complete synchronization for the two states of the slave system.