Chaotic dynamics of a harmonically excited spring-pendulum system with internal resonance.

*(English)*Zbl 0907.70015The specific system examined is a harmonically excited spring-pendulum system, which can be described by two nonlinear nonautonomous ordinary differential equations of the second order. The purpose is the investigation of chaotic responses in this system when some external and internal resonance conditions are fulfilled. By the method of multiple scales, the original system is reduced to an approximate autonomous system of four equations for amplitude and phase variables. The approximate system is shown to have Hopf bifurcation and transition to chaos via period-doubling bifurcations. The long-term behaviors of original and approximate system are compared by examining the largest Lyapunov exponents for both the systems.

Reviewer: S.Yanchuk (Kyïv)

##### MSC:

70K50 | Bifurcations and instability for nonlinear problems in mechanics |

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |