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

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


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.


Periodic Orbit Lyapunov Exponent Bifurcation Diagram Unstable Manifold Homoclinic Orbit 
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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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