International Symposium on Nonlinear Theory and Its Applications
Stability and Sensitivity of Synchronized States in a Network of Symmetrically Coupled Nonlinear Oscillators for Generating Gait Patterns
Masashi Ota, Sho Yasui, Sho Shirasaka, Hiroya Nakao,
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A coupled-oscillator model for the central pattern generator proposed by Golubitsky et al. , which can exhibit various synchronized states that correspond to typical quadruped gaits, is studied. The stability and sensitivity of the synchronized states are quantified by the Lyapunov exponents and the associated Lyapunov vectors. It is shown that the stability of the synchronized state depends on the gaits, and the Lyapunov vectors reflect the symmetry of the gaits. The asymptotic phase response of the model to external perturbations is characterized by the adjoint Lyapunov vector associated with the zero Lyapunov exponent. Phase response properties of the gait measured by direct numerical stimulations reasonably agree with the adjoint Lyapunov vectors.