Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements

Yuri Borisovich Gaididei, Rainer Berkemer, C. Gorria, Peter Leth Christiansen, A. Kawamoto, T. Shiga, Mads Peter Sørensen, Jens Starke

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Abstract

The dynamics of asymmetrically coupled nonlinear elements is considered. It is shown that there are two distinctive regimes of oscillatory behavior of one-way nonlinearly coupled elements depending on the relaxation time and the strength of the coupling. In the subcritical regime when the relaxation time is shorter than a critical one a spatially uniform stationary state is stable. In the supercritical regime due to a Hopf bifurcation traveling waves spontaneously create and propagate along the system. Our analytical approach is in good agreement with numerical simulations of the fully nonlinear model.
Original languageEnglish
JournalDiscrete and Continuous Dynamical Systems. Series S
Volume4
Issue number5
Pages (from-to)1167-1179
ISSN1937-1632
DOIs
Publication statusPublished - 2011

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