Stochastic Theory of Transition Phenomena in Nonequilibrium Systems

  • G. Nicolis
  • C. Van den Broeck
Part of the NATO ASI Series book series (NSSB, volume 116)


Cooperative behaviour in nature is intimately connected with the ability of large classes of dynamical systems to undergo transitions towards qualitatively different types of behaviour. The most familiar example is primary bifurcation (see also lectures by P. Fife and L. Lugiato). Let
$$\frac{{\partial \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{X} }} {{\partial t}} =\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{F}\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{X},\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\lambda } )$$
be a dynamical system in which X̰ is the set of state variables viewed as a vector in an appropriate space, F̰ a functional acting on X̰, and λ̰ a set of parameters through which the system can be controlled externally. Among the multitude of solutions that may be available, we isolate a particular reference state X̰s, because of its simplicity or its physical importance. For instance, in an autonomous system subject to a homogeneous environment, X̰s may represent a uniform steadystate solution.


Spatial Correlation Correlation Length Master Equation Bifurcation Point Entropy Production 
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Transient phenomena

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Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • G. Nicolis
    • 1
  • C. Van den Broeck
    • 2
  1. 1.Faculté des Sciences, CP 226, Campus PlaineUniversité Libre de BruxellesBruxellesBelgium
  2. 2.Dept. Nat.Vrije Universiteit BrusselBrusselBelgium

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