64 citations · 356 across the 30 of their papers we have counts for
5 papers · 1 filter
Isostables for stochastic oscillators
Alberto Pérez-Cervera, Benjamin Lindner, Peter J. Thomas
Thomas and Lindner (2014, Phys.Rev.Lett.) defined an asymptotic phase for stochastic oscillators as the angle in the complex plane made by the eigenfunction, having a complex eigen…
A Partial Differential Equation for the Mean--Return-Time Phase of Planar Stochastic Oscillators
Alexander Cao, Benjamin Lindner, Peter J. Thomas
Stochastic oscillations are ubiquitous in many systems. For deterministic systems, the oscillator's phase has been widely used as an effective one-dimensional description of a high…
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…
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…
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…