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ID 117907
Author
Yoshikawa, Masaki Tokushima University
Ono, Kentaro Tokushima University
Keywords
Wilson-Cowan model
bifurcation
brute-force analysis
torus
chaos
entrainment
Content Type
Journal Article
Description
We investigate bifurcations of periodic solutions observed in the forced Wilson-Cowan neuron pair by both the brute-force computation and the shooting method. By superimposing the results given by both methods, a detailed topological classification of periodic solutions is achieved that includes tori and chaos attractors in the parameter space is achieved. We thoroughly explore the parameter space composed of threshold values, amplitude, and angular velocity of an external forcing term. Many bifurcation curves that are invisible when using brute-force method are solved by the shooting method. We find out a typical bifurcation structure including Arnold tongue in the angular velocity and the amplitude of the external force parameter plane, and confirm its fractal structure. In addition, the emergence of periodic bursting responses depending on these patterns is explained.
Journal Title
Nonlinear Theory and Its Applications, IEICE
ISSN
21854106
Publisher
The Institute of Electronics, Information and Communication Engineers
Volume
14
Issue
2
Start Page
366
End Page
377
Published Date
2023-04-01
Remark
This work is licensed under a Creative Commons Attribution NonCommercial, No Derivatives 4.0 License (https://creativecommons.org/licenses/by-nc-nd/4.0/deed).
Rights
©IEICE 2023
EDB ID
DOI (Published Version)
URL ( Publisher's Version )
FullText File
language
eng
TextVersion
Publisher
departments
Center for Administration of Information Technology