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.
|Journal||Discrete and Continuous Dynamical Systems. Series S|
|Publication status||Published - 2011|
Gaididei, Y. B., Berkemer, R., Gorria, C., Christiansen, P. L., Kawamoto, A., Shiga, T., ... Starke, J. (2011). Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements. Discrete and Continuous Dynamical Systems. Series S, 4(5), 1167-1179. https://doi.org/10.3934/dcdss.2011.4.1167