رویکرد جهانی به غلبه بر بی حرکتی،بی ثباتی و غیرمارکوفی از فرآیندهای تصادفی در سیستم های پیچیده

In the present paper, we suggest a new universal approach to study complex systems by microscopic, mesoscopic and macroscopic methods. We discuss new possibilities of extracting information on nonstationarity, unsteadiness and non-Markovity of discrete stochastic processes in complex systems. We consider statistical properties of the fast, intermediate and slow components of the investigated processes in complex systems within the framework of microscopic, mesoscopic and macroscopic approaches separately. Among them theoretical analysis is carried out by means of local noisy time-dependent parameters and the conception of a quasi-Brownian particle (QBP) (mesoscopic approach) as well as the use of wavelet transformation of the initial row time series. As a concrete example we examine the seismic time series data for strong and weak earthquakes in Turkey (1998,19991998,1999) in detail, as well as technogenic explosions. We propose a new possible solution to the problem of forecasting strong earthquakes. Besides we have found out that an unexpected restoration of the first two local noisy parameters in weak earthquakes and technogenic explosions is determined by exponential law. In this paper we have also carried out the comparison and have discussed the received time dependence of the local parameters for various seismic phenomena.

Nonstationarity, unsteadiness and non-Markovity are the most common essential peculiarities of stochastic processes in nature. The existence of similar properties creates significant difficulties for the theoretical analysis of real complex systems [1]. At present, methods connected with localization of the registered or calculated parameters for the quantitative account of the dramatic changes caused by the fast alternation of the behavior modes and intermittency came into use. For example, the time behavior of the local (scale) Hurst exponents was found in the recent work of Stanley et al. to study multifractal cascades in heartbeat dynamics [1] and to analyze and forecast earthquakes and technogenic explosions in Ref. [2]. The application of the local characteristics allows to avoid difficulties connected with nonergodicity of the investigated system and gives a possibility to extract additional valuable information on the hidden properties of real complex systems. From the physical point of view this approach resembles the use of nonlinear equations of generalized hydrodynamics with the local time behavior of hydrodynamical and thermodynamical parameters and characteristics. It is well known that one of the major problems of seismology is to predict the beginning of the main shock. Although science still seems to be far from the guaranteed decision of this problem there exist some interesting approaches based on the peculiar properties of precursory phenomena [3], [4], [5], [6], [7], [8] and [9]. Another important problem is recognition and differentiation of weak earthquakes and technogenic underground explosion signals. One of the useful means of solving this problem is by defining their local characteristics [1] and [2]. In the present work we suggest a new universal description of real complex systems by means of the microscopic, mesoscopic and macroscopic methods. We start with a macroscopic approach based on the kinetic theory of discrete stochastic processes and the hierarchy of the chain of finite-difference kinetic equations for the discrete time correlation function (TCF) and memory functions [2], [10] and [11]. The mesoscopic phenomena of the so-called “soft matter” physics, embracing a diverse range of system including liquid crystals, colloids, and biomembranes, generally involve some form of coupling of different characteristic time- and length-scales. Computational modelling of such multi-scale effects requires a new methodology applicable beyond the realm of traditional techniques such as ab initio and classical molecular dynamics (the methods of choice in the microscopic regime), as well as phase field modelling or the lattice-Boltzmann method (usually concerned with the macroscopic regime). We propose to consider intermediate and slow processes within a unified framework of mesoscopic approach: by means of local time behavior of the local relaxation and kinetic parameters, local non-Markovity parameters and so on. For this purpose we introduce the notion of quasi-Brownian motion in a complex system by coarse-grained averaging of the initial time series on the basis of wavelet transformation. As an example we consider here the local properties of relaxation or noise parameters for the analysis of seismic phenomena such as earthquakes and technogenic explosions. The layout of the paper is as follows. In Section 2 we describe in brief the stochastic dynamics of time correlation in complex systems containing seismic signals by means of discrete non-Markov kinetic equations. The basic equations used for these calculations are presented here. The local noise parameters are defined in Section 3. Section 4 contains the results obtained by the local noise parameter procedure. The models of the time dependence of the local parameters are given in Section 5. The basic conclusions are discussed in Section 6.

In this work a universal method for investigating nonstationary, unsteady and non-Markov random processes in discrete systems is suggested. This universality is achieved by combining the opportunities of microscopic, mesoscopic and macroscopic descriptions for complex systems. This method allows to find and to analyze fast, slow and superslow processes. To investigate superslow processes we propose to use the model of “a quasi-Brownian particle” which moves chaotically in heat. The wavelet-transformation of the initial time series and generalized kinetic Langeven equation can be used for this purpose. This method helps to analyze and differentiate similar signals of different origin. Theoretical investigations have been realized by means of two methods supplementing each other: the statistical theory of discrete non-Markov stochastic processes [2] and the local noisy parameters. The application of the last method gives a possibility to study nonstationary and unsteady processes with alternation and superimposition of different modes. The correlation between the time scales characteristic of different modes may be different. However, if accurately realized, the localization procedure of the parameters and the calculation of their dynamics allow, as a rule, to separate the noise and the signals [1] and [2], and to carry out their quantitative and informative analysis. Another important advantage of the method is the possibility to operate it in a “real-time” regime, i.e., it can be put into practice immediately after obtaining the data, which is of great practical value. The developed approach has been tested for strong and weak EQs data and nuclear underground TEs. As a result we have obtained the following results. The time behavior of the local relaxation parameters can be described by simple model relaxation functions. The temporal relaxation of parameters λ1(t)λ1(t) and Λ1(t)Λ1(t) in weak EQs and TEs after the beginning of the “event” occurs according to the exponential law. However, the restoration and duration of the events are practically the same in the case of weak EQs. The restoration time of parameters λ1(t)λ1(t) and Λ1(t)Λ1(t) in the case of TEs differs noticeably from the duration of the event. Thus, this approach can be useful in recognition of these two different seismic phenomena. From the analysis of strong EQ data one can see that the behavior of all parameters changes greatly long before the EQ. For example, such a change for the EQ(T) presented here occurs View the MathML source∼3.5min before the main event. This change of λi(t)λi(t) and Λi(t)Λi(t) obtained for strong EQs opens the possibility for a more accurate registration of the beginning of changes of the parameters before the visual wavelet and real EQs. We are sure that the suggested method can be very useful for the study of a wide class of random discrete processes in real complex systems of live and of lifeless things: in cardiology, physiology, neurophysiology, biophysics of membranes and seismology.