Quasi-particle description of correlations and statistical memory effects in the discrete time dynamics of complex non-physical systems

We present the main provisions and ideas of the quasi-particle description concept of the discrete time dynamics of complex non-physical systems, developed within the frameworks of Memory Functions Formalism. The initial signal generated by a complex system is represented as time variations of the quasiparticle movement coordinate in one-dimensional space. The novelty of the proposed concept lies in the derivation of analytical expressions for chains of finite-difference equations relating time correlation functions and statistical memory functions for a sequence of derivatives of the temporal dynamics of the quasiparticle coordinates: velocity, acceleration, energy, energy flow. The proposed concept was tested for the study of correlations and statistical memory effects, as well as relaxation patterns, in the dynamics of neuromagnetic responses of healthy subjects and a patient with photosensitive epilepsy in response to a red-blue flickering stimulus. The results obtained allow establishing informationally significant sensors and the corresponding zones of localization of the human cerebral cortex for the analysis and diagnosis of photosensitive epilepsy.