Mixed-mode oscillations in a slow-fast flexible joint system with time delay

Abstract eng:
Mixed-mode oscillations (MMOs) are observed in a delay-coupled flexible joint system with multiple time scales, which behaves as a complex oscillatory pattern consisting of small amplitude oscillations followed by large excursions of relaxation type in a period. The existence of homoclinic orbits induced by Bogdanov-Takens bifurcation of the fast subsystem is proposed to explain the mechanisms of the occurrence of MMOs. It is numerically proved that the small parameter in a slow-fast system influences the convergence rate of oscillatory trajectories and thus leads to the transitions of mixed-mode oscillations.

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