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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Bifurcation Analysis of Wilson-Cowan Model with Singular Impulses

Discontinuity, Nonlinearity, and Complexity 10(1) (2021) 161--172 | DOI:10.5890/DNC.2021.03.012

Marat Akhmet , Sabahattincag

Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey

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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.


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