## Phase reduction and phase-based optimal control for biological systems: a tutorial

- Bharat Monga, Dan Wilson, Tim Matchen, Jeff Moehlis
- Biological Cybernetics
- 2018

@article{Shaw2012PhaseRI, title={Phase Resetting in an Asymptotically Phaseless System: On the Phase Response of Limit Cycles Verging on a Heteroclinic Orbit}, author={Kendrick M. Shaw and Youngmin Park and Hillel J. Chiel and Peter J. Thomas}, journal={SIAM J. Applied Dynamical Systems}, year={2012}, volume={11}, pages={350-391} }

- Published 2012 in SIAM J. Applied Dynamical Systems
DOI:10.1137/110828976

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 (extended dwell times in localized regions of phase space). Proximity of a limit cycle to one or more saddle equilibria can have a profound effect on the timing of trajectory components and response to both fast and slow perturbations, providing a possible mechanism for adaptive control of rhythmic motions. Reyn… CONTINUE READING