Multistability and its control in a Van Der Pol oscillator coupled with Duffing oscillator through the velocity

Self-sustained electromechanical transducers are generally built using coupled oscillators made of Van Der Pol and Duffing. In this paper, the complex dynamics of a Van Der Pol oscillator coupled with the Duffing (VDPCD) oscillator through the velocity is investigated. By exploiting nonlinear analysis techniques, several nonlinear phenomena uncovered in such types of systems are found. Among others, we have broken symmetry inducing multistability in the coupled oscillators, the phenomenon of coexisting bubble bifurcations. By employing Helmholtz’s theorem, a Hamilton energy function for the coupled model was derived. Furthermore, the famous theory of the linear augmentation method, based on the unstable equilibria of the uncontrolled model, is exploited to control the multistability of the coupled oscillators toward a regulator or a chaotic regime. A PSpice circuit was used to perform a circuit experiment, from which the results of the multistability exhibited by the coupled oscillators were further supported. At last, a microcontroller board-based experimental circuit was constructed, and the findings were corroborated by the results of the study.