Onset and chaos of the propagating pulse wave in a ring of coupled bistable oscillators

Abstract

Various propagating wave phenomena such as chaotic pulse wave propagation and propagation of phase-inversion wave have been investigated. A basic question concerning these systems is the condition under which propagating wave can emerge. It is known as propagation failure phenomenon that propagating wave fails to propagate below a certain coupling strength. In our previous research, we found by computer simulation, the propagating pulse wave in an inductor-coupled bistable oscillator system, and confirmed that it existed in comparatively large parameter region. It is robust against fluctuation and noise for relatively large coupling factor. Namely, there exists a standing pulse wave for weak coupling case, and as the value of coupling strength increases beyond a certain critical value, a propagating pulse wave appears in some parameter region. In this study, we focus our attention on the formation mechanism of propagating pulse wave. As an example, we investigate one of the onset mechanisms of propagating pulse wave for the ring of six-coupled bistable oscillator case with the aid of bifurcation theory. As a result, we have found that a global bifurcation of maps based on the heteroclinic tangle in conjunction with pitchfork bifurcation, converts the fixed point corresponding to the standing pulse wave to the invariant circle corresponding to the propagating pulse wave. In addition, we demonstrate the chaotic propagating pulse wave for large coupling factor whose propagating direction changes randomly. We calculate probability density of one-span length and investigate the mechanism of chaotically propagating pulse wave.

About the Speaker

Prof. Tetsuro Endo
Department of Electronics and Bioinformatics Meiji University,
Kawasaki, 214-8571 Japan
endoh@isc.meiji.ac.jp

Prof. Tetsuro Endo received the B.E., M.E. and Dr. Eng. degrees in Electrical Engineering from Keio University, Yokohama, Japan in 1972, 1974 and 1977, respectively. From 1977 to 1992, he was with the Department of Electrical Engineering, National Defense Academy, Yokosuka, Japan where he was an Assistant Professor, a Lecturer, and an Associate Professor. In April 1992, he joined the Department of Electronics and Communication, Faculty of Science and Technology, Meiji University, Kawasaki, Japan, as a Professor. His research interests include the study of nonlinear dynamics and chaos of coupled oscillators and phase-locked loops. From 1986 to 1989, he served as a Secretary of the Technical Group on Nonlinear Problems of IEICE. From 1995 to 1997, he was an Associate Editor of IEEE Transactions on Circuits and Systems. From 1996 to 1998, he served as a Vice Chairperson and Chairperson of the Technical Group on Nonlinear Problems of IEICE. From 2006 to 2008, he served as a Vice President of the Fundamentals Society of IEICE. In 2006, he was elected as a Fellow of IEICE. Dr. Endo is a senior member of IEEE.