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Complex Attractors and Patterns in Reaction–Diffusion Systems

  • Sergey Vakulenko
Article

Abstract

We consider semiflows generated by initial boundary value problems for reaction–diffusion systems. In these systems, reaction terms satisfy general conditions, which admit a transparent chemical interpretation. It is shown that the semiflows generated by these initial boundary value problems exhibit a complicated large time behavior. Any structurally stable finite dimensional dynamics (up to an orbital topological equivalence) can be realized by these semiflows by a choice of appropriate external sources and diffusion coefficients (nonlinear terms are fixed). Results can be applied to the morphogenesis and pattern formation problems.

Notes

Acknowledgments

The author is grateful to Referee for useful remarks which helped to improve the paper.

The author was financially supported by Government of Russian Federation, Grant 074-U01, also supported in part by Grant RO1 OD010936 (formerly RR07801) from the US NIH and by Grant 16-01-00648 of Russian Fund of Basic Research.

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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Institute for Mechanical Engineering ProblemsSaint PetersburgRussia
  2. 2.ITMO UniversitySaint PetersburgRussia

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