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

convoLution 

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References

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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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