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

Publication: Research - peer-reviewJournal article – Annual report year: 2011

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Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements. / Gaididei, Yuri Borisovich; Berkemer, Rainer; Gorria, C.; Christiansen, Peter Leth; Kawamoto, A.; Shiga, T.; Sørensen, Mads Peter; Starke, Jens.

In: Discrete and Continuous Dynamical Systems. Series S, Vol. 4, No. 5, 2011, p. 1167-1179.

Publication: Research - peer-reviewJournal article – Annual report year: 2011

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Gaididei, Yuri Borisovich; Berkemer, Rainer; Gorria, C.; Christiansen, Peter Leth; Kawamoto, A.; Shiga, T.; Sørensen, Mads Peter; Starke, Jens / Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements.

In: Discrete and Continuous Dynamical Systems. Series S, Vol. 4, No. 5, 2011, p. 1167-1179.

Publication: Research - peer-reviewJournal article – Annual report year: 2011

Bibtex

@article{87f315486db24deba7e09b0df83cba44,
title = "Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements",
publisher = "American Institute of Mathematical Sciences",
author = "Gaididei, {Yuri Borisovich} and Rainer Berkemer and C. Gorria and Christiansen, {Peter Leth} and A. Kawamoto and T. Shiga and Sørensen, {Mads Peter} and Jens Starke",
year = "2011",
doi = "10.3934/dcdss.2011.4.1167",
volume = "4",
number = "5",
pages = "1167--1179",
journal = "Discrete and Continuous Dynamical Systems. Series S",
issn = "1937-1632",

}

RIS

TY - JOUR

T1 - Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements

A1 - Gaididei,Yuri Borisovich

A1 - Berkemer,Rainer

A1 - Gorria,C.

A1 - Christiansen,Peter Leth

A1 - Kawamoto,A.

A1 - Shiga,T.

A1 - Sørensen,Mads Peter

A1 - Starke,Jens

AU - Gaididei,Yuri Borisovich

AU - Berkemer,Rainer

AU - Gorria,C.

AU - Christiansen,Peter Leth

AU - Kawamoto,A.

AU - Shiga,T.

AU - Sørensen,Mads Peter

AU - Starke,Jens

PB - American Institute of Mathematical Sciences

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

U2 - 10.3934/dcdss.2011.4.1167

DO - 10.3934/dcdss.2011.4.1167

JO - Discrete and Continuous Dynamical Systems. Series S

JF - Discrete and Continuous Dynamical Systems. Series S

SN - 1937-1632

IS - 5

VL - 4

SP - 1167

EP - 1179

ER -