Scattering of particlelike patterns in dissipative systems is studied, especially we focus on the issue how the input-output relation is controlled at a head-on collision in the one-dimensional(1D) space where traveling pulses interact strongly. It remains an open problem due to the large deformation of patterns at a colliding point. We found that a special type of steady or time-periodic solutions called separators and their stable and unstable manifolds direct the traffic flow of orbits. Such separators are, in general, highly unstable even in the 1D case which causes a variety of input-output relations through the scattering process. We illustrate the ubiquity of separators by using the Gray-Scott model and a three-component reaction diffusion model arising in gas-discharge phenomena.
|Number of pages||1|
|Journal||Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics|
|Publication status||Published - 2003|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics