Bifurcation routes to chaos of 2-coupled oscillators and stabilization of unstable periodic orbits embedded in the chaotic attractor

This paper investigates two bifurcation routes to chaos observed in a 2-coupled oscillator system. This system has two nonlinear oscillators with fifth-power nonlinear conductance and third-power nonlinear inductance, and hence can be represented as a 4th-order nonlinear autonomous system. In particular, this system has a positive parameter “ε” showing the degree of nonlinearity. We have found out two distinct bifurcation routes to chaos starting from the same phase and the reverse phase attractors as ε is increased. Further, we apply OGY-method to stabilize some unstable periodic orbits embedded in the chaotic attractor