The theory of a flux steady-state related to avalanche formation is presented for the simplest model of a sand pile within the framework of the Lorenz approach. The stationary values of sand velocity and sand pile slope are derived as functions of a control parameter (driven sand pile slope)....

Mutually conjugated synergetic schemes are assumed to address the evolution of nonequilibrium self-organizing system. Within the framework of the former, the system is parameterized by a conserving order parameter using density, a conjugate field reducing to a gradient of related flux, and...

The general approach of a nonlinear Fokker–Planck equation is applied to investigate the behavior of main statistical moments of a stochastic system. It was shown that the system described by Tsallis statistics can undergo transitions inherent to multiplicative noise-induced transitions. The...

On the basis of Langevin equation the optimal SUSY field scheme is formulated to describe a non-equilibrium thermodynamic system with quenched disorder and non-ergodicity effects. Thermodynamic and isothermal susceptibilities, memory parameter and irreversible response are determined at...

The behaviour of most probable values of the order parameter x and the amplitude of the conjugate force fluctuations φ is studied for a stochastic system with a coloured multiplicative noise and absorbing state. The phase diagrams introduced as dependencies of the noise self-correlation time...