Bifurcation Analysis of Wilson-Cowan Model with Singular Impulses

AKHMET M., Çağ S.

Discontinuity, Nonlinearity, and Complexity, vol.10, no.1, pp.161-172, 2021 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.5890/dnc.2021.03.012
  • Journal Name: Discontinuity, Nonlinearity, and Complexity
  • Journal Indexes: Scopus
  • Page Numbers: pp.161-172
  • Keywords: Bifurcation of attractors, Medusas, Rings, Singular impulses, Singular Wilson-Cowan model
  • Middle East Technical University Affiliated: Yes

Abstract

© 2021 L&H Scientific Publishing, LLC. All rights reserved.The paper concerns with Wilson-Cowan neural model. The main novelty of the study is that besides the traditional singularity of the model, we consider singular impulses. A new technique of analysis of the phenomenon is suggested. This allows to consider the existence of solutions of the model and bifurcation in ultimate neural behavior observed through numerical simulations. The bifurcations are reasoned by impulses and singularity in the model and they concern the structure of attractors, which consist of newly introduced sets in the phase space such that medusas and rings.