TY - JOUR
T1 - Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements
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
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
M3 - Journal article
SN - 1937-1632
VL - 4
SP - 1167
EP - 1179
JO - Discrete and Continuous Dynamical Systems. Series S
JF - Discrete and Continuous Dynamical Systems. Series S
IS - 5
ER -