Nonlinear equations of reaction-diffusion type for neural populations
| Autor: | Katsuyuki Katayama, Takuji Kawahara, Tokuji Nogawa |
|---|---|
| Rok vydání: | 1983 |
| Předmět: |
Stochastic partial differential equation
Nonlinear system Multigrid method Quantitative Biology::Neurons and Cognition General Computer Science Differential equation Mathematical analysis Delay differential equation Exponential integrator Differential algebraic equation Biotechnology Mathematics Numerical partial differential equations |
| Zdroj: | Biological Cybernetics. 48:19-25 |
| ISSN: | 1432-0770 0340-1200 |
| DOI: | 10.1007/bf00336881 |
| Popis: | Several simplified differential equations are derived from the Wilson and Cowan model describing the dynamics of excitatory and inhibitory neurons. It is shown, by expansions of the convolution integrals and the input-output functions, that the basic integrodifferential equations can be reduced to two coupled nonlinear partial differential equations of reaction-diffusion type. Further simplification leads to the coupled partial differential equations mathematically equivalent to the FitzHugh-Nagumo equations for the nerve impulse. Through a brief stability analysis in relation to the existing investigations on the bifurcation phenomena, an attempt is made to clarify the consequence due to the approximations introduced in this paper. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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