Birth of oscillation in coupled non-oscillatory Rayleigh–Duffing oscillators

Guin, Arun Kanti; Dandapathak, M.; Sarkar, Shrabana; Sarkar, B. C.

doi:10.1016/j.cnsns.2016.06.002

Cited by 23 publications

(2 citation statements)

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“…The mathematical model of the pair of mutually coupled Rayleigh-Duffing oscillators discussed in this work [10], consists of the following pair of second order nonlinear differential equations: we can rewrite system (1) in the form:…”

Section: System Model and Basic Properties 21 System Modelmentioning

confidence: 99%

“…The occurrence of generalized synchronization has been proved through the 'auxiliary' slave system approach for nonlinear analysis. Guin and coworkers [10] studied the dynamics of a pair of bilaterally coupled non-oscillatory Rayleigh-Duffing oscillators, with particular attention on the effects of coupling in inducing oscillatory states. Considering direct and anti-diffusive coupling cases, the authors derived conditions for periodic bifurcation in parameter space involving the coupling factor and the linear damping parameter of the RDOs.…”

Section: Introductionmentioning

confidence: 99%

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On the mechanism of multiscroll chaos generation in coupled non-oscillatory rayleigh-duffing oscillators

Ramakrishnan¹,

Telem²,

Kengne³

et al. 2022

Phys. Scr.

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We investigate the dynamics of a pair of coupled non oscillatory Rayleigh-Duffing oscillators (RDOs here after). The RDO serves as a model for a class of nonlinear oscillators including microwave Gunn oscillators [Guin et al., Comm. in Nonlinear Sci. Numerical Simulat, 2017]. Here, the coupling between the two oscillators is obtained by superimposing to each one’s amplitude a perturbation proportional to the other one. We demonstrate that the coupling induces more equilibrium points and results in extremely complex nonlinear behaviors including multistability (up to six coexisting attractors), multiple Hopf bifurcations, multi-scroll chaos, and coexisting bifurcation trees. These phenomena are studied in detail by utilizing one-parametric bifurcation plots, bi-parametric Lyapunov exponent diagrams, phase space trajectory plots, and basins of attraction as well. Experimental results captured from an Arduino microcontroller-based realization of the coupled RDOs are included to support the observations made through numerical analysis. We would like to point out that the coupling scheme followed in this work may stimulate the research on multiscroll chaos generation based on coupled nonlinear oscillators.

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Section: System Model and Basic Properties 21 System Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%