Abstract
This paper is concerned with the analysis of the displayed nonlinear phenomena, chaos and bifurcations, in the planar passive dynamic walking of the planar compass-gait biped model under a leg length asymmetry as it goes down an inclined surface. The passive dynamic walking of the compass-gait model is modelled with an impulsive hybrid nonlinear dynamics. In this work, we present a normalised dynamics expressed in terms of dimensionless ratios. Our analysis and simulation of the passive bipedal gaits is realised mainly through bifurcation diagrams where a normalised leg length discrepancy is adopted as the bifurcation parameter. We report the exhibition of complex behaviours, namely the period-doubling bifurcation (PDB), the cyclic-fold bifurcation (CFB), the period-doubling route to chaos, the period-remerging scheme, the boundary crisis (BC), etc. We demonstrate also the exhibition of the Neimark-Sacker-2 bifurcation by investigating the tendency of the characteristic multipliers of the Jacobian matrix of the Poincare map.
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