Master-slave synchronization in the Duffing-van der Pol and Φ⁶Duffing oscillators

Abstract

In this work a master-slave configuration to obtain synchronization between the double-well Duffing-van der Pol (master system) and the three-well Φ6 Duffing oscillators (slave system) is studied. For this configuration, we analyze the system when the dissipative and one that combines the elastic and dissipative couplings are used. Whenever the dissipative coupling is used, we observed a vertical shift synchronization in the slave system. However, when the combination of the elastic and dissipative couplings is used, the vertical shift disappears obtaining complete synchronization. We resort to perturbation method to corroborate analytically these kind of synchronization, when the master system provides an harmonic function to the slave system. These synchronizations are numerically corroborated.