Structural turbulence in boundary value problems

Consideration is given to certain boundary value problems for a PDE description of the turbulent processes in ideal media, specifically, in idealized electric circuits with distributive parameters. We describe properties of attractors of individual trajectories and of a global attractor for the infinite dimensional dynamical system induced by these problems. In particular, we evaluate their topological characteristics (entropy, fractal dimension, etc.). We discuss scenarios for self-birthing structures and describe the spatial-temporal evolution of structures. We consider a self-stochasticity phenomenon based on the fact that the attractor of a deterministic system contains random functions.