Dynamic properties of VDP-CPG model in rhythmic movement with delay

Liqin Liu; Chunrui Zhang; Liqin Liu; Chunrui Zhang

doi:10.3934/mbe.2020181

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 4: 3190-3202. doi: 10.3934/mbe.2020181

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Dynamic properties of VDP-CPG model in rhythmic movement with delay

Liqin Liu ,
Chunrui Zhang ^,

Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Received: 17 March 2020 Accepted: 16 April 2020 Published: 23 April 2020

In this paper, Van Der Pol (VDP) oscillators are used as the output signal of central pattern generator (CPG), and a VDP-CPG network system of quadruped with four primary gaits (walk, trot, pace and bound) is established. The existence conditions of Hopf bifurcations for VDP-CPG systems corresponding to four primary gaits are given, and the coupling strength ranges between oscillators for four gaits are obtained. Numerical simulations are used to support theoretical analysis.
- VDP-CPG,
- rhythmic movement,
- gait,
- hopf bifurcation
Citation: Liqin Liu, Chunrui Zhang. Dynamic properties of VDP-CPG model in rhythmic movement with delay[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 3190-3202. doi: 10.3934/mbe.2020181

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Abstract

In this paper, Van Der Pol (VDP) oscillators are used as the output signal of central pattern generator (CPG), and a VDP-CPG network system of quadruped with four primary gaits (walk, trot, pace and bound) is established. The existence conditions of Hopf bifurcations for VDP-CPG systems corresponding to four primary gaits are given, and the coupling strength ranges between oscillators for four gaits are obtained. Numerical simulations are used to support theoretical analysis.

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