Shape versus timing: linear responses of a limit cycle with hard boundaries under instantaneous and static perturbation.

ABSTRACT: 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 that make and break contact with a constraint surface. Examples include heel-ground interaction in locomotion, firing rate rectification in neural networks, and stick-slip oscillators. In many rhythmic systems, robustness against external perturbations involves response of both the shape and the timing of the limit cycle trajectory. The existing methods of infinitesimal phase response curve (iPRC) and variational analysis are well established for quantifying changes in timing and shape, respectively, for smooth systems. These tools have recently been extended to nonsmooth dynamics with transversal crossing boundar

SUBMITTER: Wang Y 

PROVIDER: S-EPMC10194846 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature