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Volume 25, Issue 4
Standing Wave Solutions in Nonhomogeneous Delayed Synaptically Coupled Neuronal Networks

Linghai Zhang & Melissa Anne Stoner

DOI: 10.4208/jpde.v25.n4.1

J. Part. Diff. Eq., 25 (2012), pp. 295-329.

Published online: 2012-12

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  • Abstract

The authors establish the existence and stability of standing wave solutions of a nonlinear singularly perturbed systemof integral differential equations and a nonlinear scalar integral differential equation. It will be shown that there exist six standing wave solutions (u(x,t),w(x,t))=(U(x),W(x)) to the nonlinear singularly perturbed system of integral differential equations. Similarly, there exist six standing wave solutions u(x,t)=U(x) to the nonlinear scalar integral differential equation. The main idea to establish the stability is to construct Evans functions corresponding to several associated eigenvalue problems.

  • Keywords

Nonhomogeneous synaptically coupled neuronal networks standing wave solutions existence stability eigenvalue problems Evans functions

  • AMS Subject Headings

92C20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

liz5@lehigh.edu (Linghai Zhang)

mastoner@salisburg.edu (Melissa Anne Stoner)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-25-295, author = {Zhang , Linghai and Stoner , Melissa Anne}, title = {Standing Wave Solutions in Nonhomogeneous Delayed Synaptically Coupled Neuronal Networks}, journal = {Journal of Partial Differential Equations}, year = {2012}, volume = {25}, number = {4}, pages = {295--329}, abstract = {

The authors establish the existence and stability of standing wave solutions of a nonlinear singularly perturbed systemof integral differential equations and a nonlinear scalar integral differential equation. It will be shown that there exist six standing wave solutions (u(x,t),w(x,t))=(U(x),W(x)) to the nonlinear singularly perturbed system of integral differential equations. Similarly, there exist six standing wave solutions u(x,t)=U(x) to the nonlinear scalar integral differential equation. The main idea to establish the stability is to construct Evans functions corresponding to several associated eigenvalue problems.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v25.n4.1}, url = {http://global-sci.org/intro/article_detail/jpde/5188.html} }
TY - JOUR T1 - Standing Wave Solutions in Nonhomogeneous Delayed Synaptically Coupled Neuronal Networks AU - Zhang , Linghai AU - Stoner , Melissa Anne JO - Journal of Partial Differential Equations VL - 4 SP - 295 EP - 329 PY - 2012 DA - 2012/12 SN - 25 DO - http://doi.org/10.4208/jpde.v25.n4.1 UR - https://global-sci.org/intro/article_detail/jpde/5188.html KW - Nonhomogeneous synaptically coupled neuronal networks KW - standing wave solutions KW - existence KW - stability KW - eigenvalue problems KW - Evans functions AB -

The authors establish the existence and stability of standing wave solutions of a nonlinear singularly perturbed systemof integral differential equations and a nonlinear scalar integral differential equation. It will be shown that there exist six standing wave solutions (u(x,t),w(x,t))=(U(x),W(x)) to the nonlinear singularly perturbed system of integral differential equations. Similarly, there exist six standing wave solutions u(x,t)=U(x) to the nonlinear scalar integral differential equation. The main idea to establish the stability is to construct Evans functions corresponding to several associated eigenvalue problems.

Zhang , Linghai and Stoner , Melissa Anne. (2012). Standing Wave Solutions in Nonhomogeneous Delayed Synaptically Coupled Neuronal Networks. Journal of Partial Differential Equations. 25 (4). 295-329. doi:10.4208/jpde.v25.n4.1
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