Extended Fokker Planck model: properties and solutions
  In the current paper Fokker Planck model of random walks has been extended to non conservative cases characterized by explicit dependence of diffusion and energy on time. A given generalization allows describing of such non equilibrium processes as Levy flights in a classical differential form without use of fractal PDE. Besides it takes into account mixing properties that are obligatory for a certain class of chaotic systems such as Kolmogorov K system. It was shown that an abnormal transport is a consequence of the equilibrium distortion and not stationary diffusion. The particular case of fixed boundaries was considered. According to the received solutions it was shown that a system structure can resist a weak disturbance in the vicinity of the discrete regimes, defined by a system scale and its nonlinear properties. These regimes correspond to the exponential increase of quasi regular structure fluctuations. Only fast disruption of regime is possible for other states of the system. It leads to an immediate transition to the chaos. 
Sergey Kamenshchikov
nlin.CD math.PR