%0 Journal Article
%T Experiment on Bifurcation and Chaos in Coupled Anisochronous Self-Excited Systems: Case of Two Coupled van der Pol-Duffing Oscillators
%A J. Kengne
%A F. Kenmogne
%A V. Kamdoum Tamba
%J Journal of Nonlinear Dynamics
%D 2014
%R 10.1155/2014/815783
%X The analog circuit implementation and the experimental bifurcation analysis of coupled anisochronous self-driven systems modelled by two mutually coupled van der Pol-Duffing oscillators are considered. The coupling between the two oscillators is set in a symmetrical way that linearly depends on the difference of their velocities (i.e., dissipative coupling). Interest in this problem does not decrease because of its significance and possible application in the analysis of different, biological, chemical, and electrical systems (e.g., coupled van der Pol-Duffing electrical system). Regions of quenching behavior as well as conditions for the appearance of Hopf bifurcations are analytically defined. The scenarios/routes to chaos are studied with particular emphasis on the effects of cubic nonlinearity (that is responsible for anisochronism of small oscillations). When monitoring the control parameter, various striking dynamic behaviors are found including period-doubling, symmetry-breaking, multistability, and chaos. An appropriate electronic circuit describing the coupled oscillator is designed and used for the investigations. Experimental results that are consistent with results from theoretical analyses are presented and convincingly show quenching phenomenon as well as bifurcation and chaos. 1. Introduction In recent years, considerable research efforts had been devoted to the analysis of coupled limit-cycle oscillators models due to the useful insight they provide into the collective dynamics of various physical, biological, chemical, and electrical (e.g., coupled van der Pol-Duffing electrical circuit) systems [1¨C5]. The system of two coupled van der Pol oscillators is one of the canonical models exhibiting the mutual synchronisation behaviour [6]. Coupled self-oscillators demonstrate some classical effects such as phase locking of the oscillations with different ratios of the frequencies [7]. Amplitude death or quenching is possible in case of dissipative coupling [8, 9]. This phenomenon has been observed experimentally in the system of coupled electromechanical oscillators [10], coupled electronic systems [11], and coupled biological oscillators [11] just to name a few. Multistability, chaos, and nonisochronism are some special effects of the synchronization picture presented by researchers [12¨C17]. Introducing additional nonlinearity of Duffing type in the original van der Pol equation leads to the so-called van der Pol-Duffing equation for which potential contains a component in the form of the coordinate raised to the fourth power [18¨C20]. This
%U http://www.hindawi.com/journals/jndy/2014/815783/