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

• Michelle Schatzman
Conference paper
• 168 Downloads
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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## Copyright information

© Springer-Verlag Berlin Heidelberg 1986

## Authors and Affiliations

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