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Dynamic transitions through scattors in dissipative systems.

Yasumasa Nishiura1, Takashi Teramoto, Kei-Ichi Ueda

  • 1Research Institute for Electronic Science, Hokkaido University, Sapporo 060-0812, Japan. nishiura@aurora.es.hokudai.ac.jp

Chaos (Woodbury, N.Y.)
|August 30, 2003
PubMed
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Particle-like patterns in dissipative systems scatter during head-on collisions. Unstable solutions called scattors and their manifolds control pattern interactions and input-output relationships, explaining complex scattering behaviors.

Area of Science:

  • Nonlinear dynamics
  • Pattern formation in dissipative systems
  • Complex systems

Background:

  • Scattering of particle-like patterns in dissipative systems is complex.
  • Controlling input-output relations during strong pattern collisions remains an open problem.
  • Large pattern deformations occur at collision points.

Purpose of the Study:

  • Investigate how input-output relations are controlled during head-on collisions of traveling patterns.
  • Identify mechanisms governing pattern scattering in dissipative systems.

Main Methods:

  • Analysis of unstable steady or time-periodic solutions (scattors).
  • Study of stable and unstable manifolds of scattors.
  • Application of models like the complex Ginzburg-Landau equation, Gray-Scott model, and a three-component reaction-diffusion model.

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Main Results:

  • Scattors and their manifolds direct the flow of pattern orbits.
  • Highly unstable scattors lead to diverse input-output relations.
  • Ubiquity of scattors demonstrated across different models.

Conclusions:

  • Scattors are key to understanding pattern scattering in dissipative systems.
  • Manifolds of scattors govern the complex dynamics of pattern interactions.
  • The findings provide a framework for predicting and controlling pattern behavior in various physical and chemical systems.