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Kinetic modeling of complex systems

Keywords:

M.B. Saikhanov – Employee of KNII of RAS. E-mail: saikhanov_musa@mail.ru Z.Sh. Gagaeva – Employee of KNII of RAS


The holistic approach for describing the complex systems on the basis of macroscopic quantization of open nonequilibrium systems and generalized principle of minimum entropy production to the nonstationary case is considered. Kinetic, stochastic and topological properties of dissipative structures that are the key for building of self-consistent theory of complex systems are analyzed. First the need of kinetic modeling of nonequilibrium systems far from equilibrium proceeding from the discrete-continuous structure of its energy spectrum is shown. The theoretical scheme that allows taking into account the inertia of an irreversible process to bring the variational equation of nonstationary evolution of open nonequilibrium systems is considered. Then the conditions at which the formation of dissipative structures occur in nonequilibrium system are analyzed. In particular it is shown that the formation of dissipative structures can occur only in a state of neutral stability of nonequilibrium system. The conditions of kinetic stability and instability of nonequilibrium system far from equilibrium are considered also. The topological properties of nonequilibrium systems, which are integral for the holistic description of complex system evolution and directly resulting from adopted for its description of discrete-continuous model, are discussed. An explanation of the physical mechanism of formation and dissipative structures restructuring under the influence from random noise is given. It is shown that the external noise contributes to dissipative structures erosion and can induce the transitions to alternative structures. The variational equation, taking into account the external effects of noise on nonequilibrium system near the stability limit, is formulated. It allows to interpret the effect of noise-induced stochastic resonance.
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