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

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  • 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.
    Mathematics Subject Classification: Primary: 34K18, 35C07, 35B36; Secondary: 37C75.


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