Chaos In Circuits And Systems
With a combination of overview, tutorial and technical articles, this book describes state-of-the-art research on significant problems in the field of chaos in circuits and systems.
TABLE OF CONTENTS Chaos In Circuits And Systems
Chapter 15: Bifurcations in Synaptically Coupled Bonh ffer-van der Pol Neurons
Kunichika Tsumoto,
Department of Electrical and Electronic Engineering, Faculty of Engineering, The University of Tokushima
Department of Radiologic Science and Engineering, School of Health Sciences, The University of Tokushima
Department of Electrical and Electronic Engineering, Faculty of Engineering, The University of Tokushima
Department of Electrical and Electronic Engineering, Faculty of Engineering, The University of Tokushima
Tokushima, 770-8506, Japan tsu@ee.tokushima-u.ac.jp
Tetsuya Yoshinaga, Department of Radiologic Science and Engineering, School of Health Sciences, The University of Tokushima
Tokushima, 770-8509, Japan yosinaga@medsci.tokushima-u.ac.jp
Hiroshi Kawakami, Department of Electrical and Electronic Engineering, Faculty of Engineering, The University of Tokushima
Tokushima, 770-8506, Japan kawakami@ee.tokushima-u.ac.jp
We investigate bifurcations of periodic solutions in model equations of two and three Bonh ffer-van der Pol (BVP) neurons coupled through characteristics of synaptic transmissions with a time delay. Bifurcations of the coupled BVP neurons are compared with bifurcations of synaptically coupled Hodgkin-Huxley neurons. We obtain a parameter set of the BVP system, such that the two systems are qualitatively very similar from a bifurcational point of view. This study provides a base for analysis of synaptically coupled neurons with a large number of coupling strategies.
15.1 Introduction
To understand information processing in the brain, synchronization of oscillatory phenomena in coupled neuronal models has been intensively investigated [1] , [2]. In this chapter, we investigate bifurcations of periodic oscillations in a model equation of Bonh ffer-van der Pol (BVP) or FitzHugh-Nagumo [3] [5] neurons coupled through the characteristics of synaptic transmissions with a time delay. Although there are many papers on synchronization phenomena in linearly coupled neuronal oscillators, relatively little has been investigated for a more realistic model describing the time-dependent conductance of the synapse [6] [8].
In [9], we have proposed a numerical method...
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