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Bifurcations, Chaos and Self-Organization in Reaction-Diffusion Systems

  • G. Nicolis
  • P. Gaspard
Part of the NATO ASI Series book series (ASIC, volume 313)

Abstract

We review recent work about temporal and spatio-temporal self-organized structures in macroscopic physico-chemical systems and their analysis in the light of recent advances in nonlinear mathematics. Chaos and mixed-mode oscillations in far- from-equilibrium chemical reactions are first described. We show how homoclinic tangencies of Sil’nikov type and associated to a cycle can help us in elucidating the complex bifurcation sequences and the related chaotic time evolution observed in these systems. A chemical kinetic example of diffusion-induced spatio-temporal chaos is presented. Finally, we discuss the conditions for pattern formation via spatial symmetry breaking in uniform and non-uniform environments.

Keywords

Periodic Orbit Lyapunov Exponent Bifurcation Diagram Unstable Manifold Homoclinic Orbit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • G. Nicolis
    • 1
  • P. Gaspard
    • 1
  1. 1.Faculté des SciencesUniversité Libre de BruxellesBruxellesBelgium

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