ArticleJournal of mathematical biology2018
Greater accuracy and broadened applicability of phase reduction using isostable coordinates.
Article in Journal of mathematical biology, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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Who cites it
10 citing papers in PubMed.
- Interspike interval correlations in neuron models with adaptation and correlated noise.PLoS computational biology · 2021Article
- Resolving molecular contributions of ion channel noise to interspike interval variability through stochastic shielding.Biological cybernetics · 2021Article
- Optimizing deep brain stimulation based on isostable amplitude in essential tremor patient models.Journal of neural engineering · 2021Article
- Shape versus timing: linear responses of a limit cycle with hard boundaries under instantaneous and static perturbation.SIAM journal on applied dynamical systems · 2021Article
- Analysis of neural clusters due to deep brain stimulation pulses.Biological cybernetics · 2020Article
- Optimal open-loop desynchronization of neural oscillator populations.Journal of mathematical biology · 2020Article
- Stabilization of Weakly Unstable Fixed Points as a Common Dynamical Mechanism of High-Frequency Electrical Stimulation.Scientific reports · 2020Article
- Recent advances in coupled oscillator theory.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2019Article
- Nonlinear phase coupling functions: a numerical study.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2019Article
- Synchronization of Electrically Coupled Resonate-and-Fire Neurons.SIAM journal on applied dynamical systems · 2019Article
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Authors and funding
2 authors.
Funding
Abstract
The applicability of phase models is generally limited by the constraint that the dynamics of a perturbed oscillator must stay near its underlying periodic orbit. Consequently, external perturbations must be sufficiently weak so that these assumptions remain valid. Using the notion of isostables of periodic orbits to provide a simplified coordinate system from which to understand the dynamics transverse to a periodic orbit, we devise a strategy to correct for changing phase dynamics for locations away from the limit cycle. Consequently, these corrected phase dynamics allow for perturbations of larger magnitude without invalidating the underlying assumptions of the reduction. The proposed reduction strategy yields a closed set of equations and can be applied to periodic orbits embedded in arbitrarily high dimensional spaces. We illustrate the utility of this strategy in two models with biological relevance. In the first application, we find that an optimal control strategy for modifying the period of oscillation can be improved with the corrected phase reduction. In the second, the corrected phase reduced dynamics are used to understand adaptation and memory effects resulting from past perturbations.
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