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Self Organizing Mathematical Models: Nonlinear Evolution Equations with a Convolution term

  • Michelle Schatzman
Conference paper
Part of the NATO ASI Series book series (volume 20)

Abstract

The simplest example of a dynamical system which organizes itself through cooperation and competition has been given in this conference C8]; I shall formalize it as follows: let A be a linear operator in the plane R 2,and consider the ordinary diferential system
$$ \dot{x} = Ax,\,x(0) = {x_0} $$
(1)
where x is constrained to remain in the unit square
$$ x\,\,\,\,K = \left[ { - 1,1} \right] \times \left[ { - 1,1} \right] $$
(2)

Keywords

Nonlinear Evolution Equation Random Wave Liapunov Function Secondary Bifurcation NeurophysioLogiCaL modeLs 
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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References

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    E. Bienenstock, Cooperation and competition in the central system development: a unifying approach, (1984) in Synergetics, Springer.Google Scholar
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    Anderson, this volumeGoogle Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Michelle Schatzman
    • 1
  1. 1.MathématiquesUniversité Claude-BernardVilleurbanne CedexFrance

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