ID 112115
Author
Tsuji, Shigeki Tokushima University|Japan Science and Technology Agency (JST)|The University of Tokyo
Keywords
Bifurcation
chaos
BVP oscillator
diffusive coupling
Content Type
Journal Article
Description
The Bonhöffer-van der Pol (BVP) oscillator is a simple circuit implementation describing neuronal dynamics. Lately the diffusive coupling structure of neurons attracts much attention since the existence of the gap-junctional coupling has been confirmed in the brain. Such coupling is easily realized by linear resistors for the circuit implementation, however, there are not enough investigations about diffusively coupled BVP oscillators, even a couple of BVP oscillators. We have considered several types of coupling structure between two BVP oscillators, and discussed their dynamical behavior in preceding works. In this paper, we treat a simple structure called current coupling and study their dynamical properties by the bifurcation theory. We investigate various bifurcation phenomena by computing some bifurcation diagrams in two cases, symmetrically and asymmetrically coupled systems. In symmetrically coupled systems, although all internal elements of two oscillators are the same, we obtain in-phase, anti-phase solution and some chaotic attractors. Moreover, we show that two quasi-periodic solutions are disappeared simultaneously by the homoclinic bifurcation on the Poincaré map and that a large quasi-periodic solution is generated by the coalescence of these quasi-periodic solutions, but it is disappeared by the heteroclinic bifurcation on the Poincaré map. In the other case, we confirm the existence a conspicuous chaotic attractor in the laboratory experiments.
Journal Title
International Journal of Bifurcation and Chaos
ISSN
02181274
17936551
NCID
AA10810319
Publisher
World Scientific
Volume
17
Issue
3
Start Page
837
End Page
850
Published Date
2007-03
Rights
Electronic version of an article published as International Journal of Bifurcation and Chaos Vol. 17, No. 3, 2007, 837-850, DOI: 10.1142/S0218127407017586 © World Scientific Publishing Company, https://www.worldscientific.com/worldscinet/ijbc
EDB ID
104057
DOI (Published Version)
URL ( Publisher's Version )
FullText File
language
eng
TextVersion
Author
departments
Center for Administration of Information Technology
Science and Technology