Self-stochasticity in deterministic boundary value problems

This paper presents the experience of applying dynamical systems theory to an investigation into nonlinear boundary value problems for partial differential equations (PDE for short) in the case that their solutions become chaotic with time. To describe the long time behavior of such solutions, the concept of self-stochasticity had been suggested. The results reported in this work are concerned linear systems of PDE with nonlinear boundary conditions; general ideas on the manner in which chaotic solutions may be described are set forth by the example of several simplest boundary value problems

On simulation of spatial-temporal chaos: The simplest mathematical patterns and computer graphics

The article presents three scenarios of the evolution of spatial-temporal chaos and specifies the corresponding types of chaotic solutions to a certain nonlinear boundary-value problem for PDE. Analytic assertions are illustrated by numerical analysis and computer graphics