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 -