Qualitative Analysis of a Quadratic Integrate-and-Fire Neuron Model with State-Dependent Feedback Control
Spiking neuron models which exhibit rich dynamics are usually defined by hybrid dynamical systems. It is revealed that mathematical analysis of these models has important significance. Therefore, in this work, we provide a comprehensively qualitative analysis for a quadratic integrate-and-fire mode...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/836402 |
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| Summary: | Spiking neuron models which exhibit rich dynamics are usually
defined by hybrid dynamical systems. It is revealed that
mathematical analysis of these models has important significance.
Therefore, in this work, we provide a comprehensively qualitative
analysis for a quadratic integrate-and-fire model by using the
theories of hybrid dynamical system. Firstly, the exact
impulsive and phase sets are defined according to the phase
portraits of the proposed model, and then the
Poincaré map is constructed. Furthermore, the
conditions for the existence and stability of an order 1 periodic
solution are provided. Moreover, the existence and nonexistence
of an order k k≥2 periodic solution have been studied
theoretically and numerically, and the results show
that the system has periodic solutions with any period. Finally,
some biological implications of the mathematical results are
discussed. |
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| ISSN: | 1026-0226 1607-887X |