1,027 research outputs found
Existence of Bistable Waves in a Competitive Recursion System with Ricker Nonlinearity
Using an abstract scheme of monotone semiflows, the existence of bistable
traveling wave solutions of a competitive recursion system with Ricker
nonlinearity is established. The traveling wave solutions formulate the strong
inter-specific actions between two competitive species
Symmetry of Traveling Wave Solutions to the Allen-Cahn Equation in \Er^2
In this paper, we prove even symmetry of monotone traveling wave solutions to
the balanced Allen-Cahn equation in the entire plane. Related results for the
unbalanced Allen-Cahn equation are also discussed
Stability, Uniqueness and Recurrence of Generalized Traveling Waves in Time Heterogeneous Media of Ignition Type
The present paper is devoted to the study of stability, uniqueness and
recurrence of generalized traveling waves of reaction-diffusion equations in
time heterogeneous media of ignition type, whose existence has been proven by
the authors of the present paper in a previous work. It is first shown that
generalized traveling waves exponentially attract wave-like initial data. Next,
properties of generalized traveling waves, such as space monotonicity and
exponential decay ahead of interface, are obtained. Uniqueness up to space
translations of generalized traveling waves is then proven. Finally, it is
shown that the wave profile of the unique generalized traveling wave is of the
same recurrence as the media. In particular, if the media is time almost
periodic, then so is the wave profile of the unique generalized traveling wave
Wave trains, self-oscillations and synchronization in discrete media
We study wave propagation in networks of coupled cells which can behave as
excitable or self-oscillatory media. For excitable media, an asymptotic
construction of wave trains is presented. This construction predicts their
shape and speed, as well as the critical coupling and the critical separation
of time scales for propagation failure. It describes stable wave train
generation by repeated firing at a boundary. In self-oscillatory media, wave
trains persist but synchronization phenomena arise. An equation describing the
evolution of the oscillator phases is derived.Comment: to appear in Physica D: Nonlinear Phenomen
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