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Qualitative Analysis of a Quadratic Integrate-and-Fire Neuron Model with State-Dependent Feedback Control
Joint Authors
Tang, Guangyao
Yang, Jin
Tang, Sanyi
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-10-01
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
Spiking neuron models which exhibit rich dynamics are usuallydefined by hybrid dynamical systems.
It is revealed thatmathematical analysis of these models has important significance.
Therefore, in this work, we provide a comprehensively qualitativeanalysis for a quadratic integrate-and-fire model by using thetheories of hybrid dynamical system.
Firstly, the exactimpulsive and phase sets are defined according to the phaseportraits of the proposed model, and then thePoincaré map is constructed.
Furthermore, theconditions for the existence and stability of an order 1 periodicsolution are provided.
Moreover, the existence and nonexistenceof an order k k≥2 periodic solution have been studiedtheoretically and numerically, and the results showthat the system has periodic solutions with any period.
Finally,some biological implications of the mathematical results arediscussed.
American Psychological Association (APA)
Tang, Guangyao& Yang, Jin& Tang, Sanyi. 2015. Qualitative Analysis of a Quadratic Integrate-and-Fire Neuron Model with State-Dependent Feedback Control. Discrete Dynamics in Nature and Society،Vol. 2015, no. 2015, pp.1-12.
https://search.emarefa.net/detail/BIM-1060783
Modern Language Association (MLA)
Tang, Guangyao…[et al.]. Qualitative Analysis of a Quadratic Integrate-and-Fire Neuron Model with State-Dependent Feedback Control. Discrete Dynamics in Nature and Society No. 2015 (2015), pp.1-12.
https://search.emarefa.net/detail/BIM-1060783
American Medical Association (AMA)
Tang, Guangyao& Yang, Jin& Tang, Sanyi. Qualitative Analysis of a Quadratic Integrate-and-Fire Neuron Model with State-Dependent Feedback Control. Discrete Dynamics in Nature and Society. 2015. Vol. 2015, no. 2015, pp.1-12.
https://search.emarefa.net/detail/BIM-1060783
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1060783