Abstract
In this work, a master-slave configuration to obtain synchronization between the Rayleigh and the Duffing oscillators is studied. For this configuration, we analyze the system when the dissipative coupling and one that combines the elastic and dissipative couplings are used. We analyzed the coupling parameters to find the range where synchronization between the oscillators is achieved. We found synchronization in the oscillators for large values of the coupling parameter. Our numerical findings show that for the dissipative coupling, there exists partial synchronization while for the others there is complete synchronization.
Highlights
Since the seminal work of Pecora and Carroll on synchronization [1], numerous works on chaos that comprises diverse areas such as lasers, chemical reactions, electronic circuits, biological systems, among others, have been studied
The hybrid function projective synchronization of chaotic systems has been developed and used on systems where the parameters of the system are unknown by applying adaptive control, A
We have studied the master-slave configuration in the Rayleigh and Duffing oscillators, when dissipative coupling is used, only complete synchronization in the projection onto the (u, v) plane can be reached
Summary
Since the seminal work of Pecora and Carroll on synchronization [1], numerous works on chaos that comprises diverse areas such as lasers, chemical reactions, electronic circuits, biological systems, among others, have been studied. The Rayleigh and Duffing oscillators are the paradigmatic circuits to study chaos in systems of low-dimensional. Studies focused on the Rayleigh oscillator reveal that it possesses a rich dynamical structure, especially when the oscillator is forced This system exhibits complex bifurcation structures with an important number of periodic states, a chaotic region and islands of periodic states, showing, in addition, transitions from chaos to stable states. Uriostegui et al [37] studied synchronization between the van der Pol and Duffing oscillators by using the elastic, dissipative and a combination of both couplings. We study and compare two types of couplings by using the Rayleigh and Duffing systems: the dissipative and the used previously by Uriostegui et al [34].
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