Phase Resetting in an Asymptotically Phaseless System: On the Phase Response of Limit Cycles Verging on a Heteroclinic Orbit

@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}
}
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