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Literature DB >> 28303309

Isochrons and phaseless sets.

Abstract

Winfree has developed mathematical models for his phase resetting experiments on biological clocks. These models lead him to ask a number of mathematical questions concerning dynamical systems. This paper deals with these mathematical questions. In Winfree's terminology we show the existence of isochrons and establish some of their properties.

Year: 2017 PMID： 28303309 DOI： 10.1007/BF01273747

Source DB: PubMed Journal: J Math Biol ISSN： 0303-6812 Impact factor: 2.259

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Cited

21 in total

1. Limitations of perturbative techniques in the analysis of rhythms and oscillations.

Authors: Kevin K Lin; Kyle C A Wedgwood; Stephen Coombes; Lai-Sang Young
Journal: J Math Biol Date: 2013-01 Impact factor: 2.259

2. Non-weak inhibition and phase resetting at negative values of phase in cells with fast-slow dynamics at hyperpolarized potentials.

Authors: Myongkeun Oh; Victor Matveev
Journal: J Comput Neurosci Date: 2010-12-04 Impact factor: 1.621

3. Action potential onset dynamics and the response speed of neuronal populations.

Authors: B Naundorf; T Geisel; F Wolf
Journal: J Comput Neurosci Date: 2005-06 Impact factor: 1.621

4. Resolving molecular contributions of ion channel noise to interspike interval variability through stochastic shielding.

Authors: Shusen Pu; Peter J Thomas
Journal: Biol Cybern Date: 2021-05-22 Impact factor: 2.086

Isochrons and phaseless sets.

1. Limitations of perturbative techniques in the analysis of rhythms and oscillations.

2. Non-weak inhibition and phase resetting at negative values of phase in cells with fast-slow dynamics at hyperpolarized potentials.

3. Action potential onset dynamics and the response speed of neuronal populations.

4. Resolving molecular contributions of ion channel noise to interspike interval variability through stochastic shielding.

5. Partial phase synchronization of neural populations due to random Poisson inputs.

6. Finding the dimension of slow dynamics in a rhythmic system.

7. Analysis of neural clusters due to deep brain stimulation pulses.

8. Greater accuracy and broadened applicability of phase reduction using isostable coordinates.

9. Minimum energy desynchronizing control for coupled neurons.

10. How to achieve fast entrainment? The timescale to synchronization.