title: Scattering and separators in dissipative systems.
abstract: 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.
authors.affiliation: Research Institute for Electronic Science, Hokkaido University, Kita-Ku, Sapporo 060-0812, Japan.
authors.forename: Yasumasa
authors.initials: Y
authors.lastname: Nishiura
authors.forename: Takashi
authors.initials: T
authors.lastname: Teramoto
authors.forename: Kei-Ichi
authors.initials: K
authors.lastname: Ueda