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

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)