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We study the influence of different delay terms in the nonlinear
(2D) diffusion equation. In the first part, the diffusive Hutchinson
equation is analyzed, where the saturation term is assumed to be delayed.
We observe a pattern forming instability showing phase turbulence at onset
followed by a secondary instability to spirals [1].
In the second part, the effect of a delayed diffusion part in the real
Ginzburg-Landau equation is examined. To
avoid short wave length divergence, 4th order spatial derivatives have to be
included. It is shown that traveling waves with a well defined phase speed occur for larger delay times. For small delay, an interesting competition between diffusive patterns and traveling waves is found. [1] M. Bestehorn, E. V. Grigorieva, and S. A. Kaschenko, Spatiotemporal structures in a model with delay and diffusion, Phys. Rev. E70, 026202 (2004) |
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