Bifurcations and chaos in two-coupled periodically driven four-well Duffing-van der Pol oscillators

Bifurcations and chaos in two-coupled periodically driven four-well Duffing-van der Pol (DVP) oscillators are numerically investigated as a function of the strength (δ) of nonlinear coupling and the amplitude (f) of the periodic driving force. The influence of weak coupling (δ ≪ 1) and strong coupling (δ ≫ 1) is analyzed with and without the external periodic force. For strong coupling (δ ≫ 1), the system shows completely chaotic behaviour but for weak coupling the system exhibits period-doubling and period-tripling routes to chaos, quasiperiodic orbit, reverse period-doubling bifurcation, periodic windows, chaotic orbit and intermittent behaviours for specific set of values of the parameters. The effect of phase shift (ϕ) of the system is also analyzed. Numerical results are demonstrated by constructing the bifurcation diagram, phase portrait and Poincare´ map.