Spontaneous periodic travelling waves in oscillatory systems with cross-diffusion

Details Spontaneous periodic travelling waves in oscillatory systems with cross-diffusion Spontaneous periodic travelling waves in oscillatory systems with cross-diffusion

2008-06-05

arxiv.org/abs/0806.0996v2

Nonlinear Sciences

Pattern Formation and Solitons

7 pages, 4 figures, as accepted to Phys Rev E 2009/10/26

Scientific paper

We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently large domain, spatially uniform oscillations in such systems are unstable with respect to small perturbations. This instability, through a transient regime appearing as spontanous focal sources, leads to establishment of periodic traveling waves. The traveling waves regime is established even if boundary conditions do not favor such solutions. The stable wavelength are within a range bounded both from above and from below, and this range does not coincide with instability bands of the spatially uniform oscillations.

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