ID 112119
Author
Ito, Daisuke The University of Shiga Prefecture
Kousaka, Takuji Oita University
Aihara, Kazuyuki The University of Tokyo
Keywords
Discrete-time hybrid dynamical system
Nagumo–Sato model
border-collision bifurcation
Content Type
Journal Article
Description
The Nagumo-Sato model is a simple mathematical expression of a single neuron, and it is categorized as a discrete-time hybrid dynamical system. To compute bifurcation sets in such a discrete-time hybrid dynamical system accurately, conditions for periodic solutions and bifurcations are formulated herewith as a boundary value problem, and Newton's method is implemented to solve that problem. As the results of the analysis, the following properties are obtained: border-collision bifurcations play a dominant role in dynamical behavior of the model; chaotic regions are distinguished by tangent bifurcations; and multi-stable attractors are observed in its coupled system. We demonstrate several bifurcation diagrams and corresponding topological properties of periodic solutions.
Journal Title
International Journal of Bifurcation and Chaos
ISSN
02181274
17936551
NCID
AA10810319
Publisher
World Scientific
Volume
26
Issue
3
Start Page
1630006
Published Date
2016-03
Rights
Electronic version of an article published as International Journal of Bifurcation and Chaos Vol. 26, No. 3, 2015, 1630006, DOI: 10.1142/S0218127416300068 © World Scientific Publishing Company, https://www.worldscientific.com/worldscinet/ijbc
EDB ID
304985
DOI (Published Version)
URL ( Publisher's Version )
FullText File
language
eng
TextVersion
Author
departments
Center for Administration of Information Technology