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

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.