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math.DS2016★ 23 cited
The Infinitesimal Phase Response Curves of Oscillators in Piecewise Smooth Dynamical Systems
Youngmin Park, Kendrick M. Shaw, Hillel J. Chiel +1
The asymptotic phase of an initial point in the stable manifold of a limit cycle identifies the phase of the point on the limit cycle to which the flow converges a…
math.DS2011★ 1 cited
Phase Resetting in an Asymptotically Phaseless System: On the Phase Response of Limit Cycles Verging on a Heteroclinic Orbit
Kendrick M. Shaw, Hillel J. Chiel, Peter J. Thomas
Rhythmic behaviors in neural systems often combine features of limit cycle dynamics (stability and periodicity) with features of near heteroclinic or near homoclinic cycle dynamics…