In this paper, we study the chaos control of pendulum system with vibration of suspension axis for ultra-subharmonic resonance by using Melnikov methods, and give a necessary condition for controlling heteroclinic chaos and homoclinic chaos, respectively. We give some bifurcation diagrams by numerical simulations, which indicate that the chaos behaviors for ultra-subharmonic resonance may be inhibited to periodic orbits by adjusting phase-difference of parametric excitation, and prove that results obtained are very effective in inhibiting chaos for ultra-subharmonic resonance.
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Phase portrait of system (2) for
The chaotic attractor of system (1) for
The bifurcation diagram of system (1) in (
The bifurcation diagram of system (1) in (
The bifurcation diagram of system (1) in (
The bifurcation diagram of system (1) in (
The bifurcation diagram of system (1) in (
The bifurcation diagram of system (1) in (