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Towards a neuromechanical model for insect locomotion: hybrid dynamical systems. (English) Zbl 1084.34050
Summary: We develop and analyze a single-degree-of-freedom model for multi-legged locomotion in the horizontal (ground) plane. The model is a hybrid dynamical system incorporating rudimentary motoneuronal activation and agonist-antagonist Hill-type muscle pairs that drive a point mass body along a line. Composition of the smooth stance phase dynamics with various discrete lift-off and touch-down protocols result in Poincaré stride-to-stride maps, and our extreme simplification of the full dynamics permits relatively complete phase plane analysis of existence and stability of periodic gaits. We use these to perform parameter studies that provide guidelines for the construction of stable periodic orbits with appropriate force and velocity signatures.

MSC:
34C60 Qualitative investigation and simulation of ordinary differential equation models
34C25 Periodic solutions to ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
92C10 Biomechanics
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