On the effect of transition from a model with concentrated parameters to a model with distributed parameters

Abstract

We note from a general point of view that adding diffusion terms to ordinary differential equations, for example, to logistic ones, can in some cases improve sufficient conditions for the stability of a stationary solution. We give examples of models in which the addition of diffusion terms to ordinary differential equations changes the stability conditions of a stationary solution.

On the Stability of Stationary States in Diffusion Models in Biology and Humanities

“…We consider the initial boundary value problem for a system of partial differential equations (see also [18,19])…”

“…Let w = (w 1 , w 2 ) be a stationary solution of the problem ( 17)- (19). Coefficients (15) of a quadratic form (14) for system (17) have the form…”