Novel Codimension-two Bifurcation in a Coupled Duffing System with Twisted frequency-response Curves

Abstract

This paper studied a novel codimension-two bifurcation combined by chaos and bifurcations of periodic orbits of period-1 and subharmonic orbits of period-2 in a coupled Duffing system with twisted frequency-response curves. A bifurcation line constructed by the saddle-node bifurcations of periodic orbits of period-1 tangentially intersects a bifurcation line constructed by the period doubling bifurcations of periodic orbits of period-1 at a codimension-two bifurcation point. Meanwhile, a Hopf bifurcation line constructed by the Hopf bifurcations of subharmonic orbits of period-2 merges into the codimension-two bifurcation point and then disappears. In this moment, chaos is generated simultaneously. To analyze the phenomenon, the periodic orbits and the subharmonic orbits are detected by using the shooting method and the frequency responses are obtained through the harmonic balance method. Besides, the stability of the obtained orbits is performed using the Floquet theory.