PSEUDOPARTICLE APPROACH IN DESCRIPTION OF DISCREPTE STOCHASTIC PROCESSES IN COMPLEX SYSTEMS

Abstract: 

We suggest here a new universal approach to study complex systems by pseudoparticle method. The initial time series we present by the set of coordinates, velocities, accelerations, kinetic energies, and flow of energies of the moving pseudoparticle. The goal of the article is to find the chain of finitedifference non-Markov kinetic equations for the time correlation functions (TCF) in terms of pseudoparticle description. Using the projection operator's technique we find the chain of finite-difference non-Markov kinetic equations for discrete pseudoparticle TCF (PTCF) and for the set of pseudoparticle discrete memory functions (PMF's). In addition, we suggest pseudoparticle the statistical quantifiers of the memory function. They allow us to extract new supplementary information about relaxation peculiarities and memory effects of the complex system in general. We hope that the developed method will be useful for the time series ana-lyses of complex systems. The developed method also has a certain preference to existing methods.

Key words: 

pseudoparticle method, discrete evolution of complex systems

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