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)....

The governed equations for the order parameter, one- and two-time correlators are obtained for systems with white multiplicative noise. We consider the noise whose amplitude depends on stochastic variable as xa where 0<a<1. It turns out that the equation for autocorrelator includes an anomalous average of the power-law function with the fractional exponent 2a. Determination of this average for the stochastic system with a self-similar phase space is performed. It is shown that at a>12, when the system is disordered, the correlator behaves in the course of...</a<1.>

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...