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math.DS2019
Shape versus timing: linear responses of a limit cycle with hard boundaries under instantaneous and static perturbation
Yangyang Wang, Jeffrey P. Gill, Hillel J. Chiel +1
When dynamical systems that produce rhythmic behaviors operate within hard limits, they may exhibit limit cycles with sliding components, that is, closed isolated periodic orbits t…
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…