Science Paper, UNVETTED!
http://www.prometheus-inc.com/asi/imaging2006/papers/temo2.pdf
IDENTIFICATION OF COMPLEX PROCESSES BASED ON
ANALYSIS OF PHASE SPACE STRUCTURES
Teimuraz Matcharashvili1,2
(matcharashvili@gtu.ge), Tamaz Chelidze1
(chelidze@ig.acnet.ge) and Manana Janiashvili3
1)Institute of Geophysics, 1 Alexidze str. 0193 Tbilisi, Georgia
2) Georgian Technical University, 77 Kostava ave. 0193, Tbilisi,Georgia
3) Institute of Cardiology, 2 Gudamakari str. 0141 Tbilisi,Georgia
Abstract.
The problem of investigation of temporal and/or spatial behavior of
highly nonlinear or complex natural systems has long been of fundamental scientific
interest. At the same time it is presently well understood that identification of
dynamics of processes in complex natural systems, through their qualitative description and quantitative evaluation, is far from a purely academic question and has an
essential practical importance. This is quite understandable as systems with complex dynamics abound in nature and examples can be found in very different areas
such as medicine and biology (rhythms, physiological cycles, epidemics), atmosphere
(climate and weather change), geophysics (tides, earthquakes, volcanoes, magnetic
field variations), economy (financial markets behavior, exchange rates), engineering
(friction, fracturing), communication (electronic networks, internet packet dynamics) etc. The past two decades of research on qualitative and especially quantitative
investigations of dynamics of real processes of different origin brought significant
progress in the understanding of behavior of natural processes. At the same time
serious drawbacks have also been revealed. This is why exhaustive investigation of
dynamical properties of complex processes for scientific, engineering or practical
purposes is now recognized as one of the main scientific challenges. Much attention
is paid to elaboration of appropriate methods aiming to measuring the complexity
of both global and local dynamical behaviors from the observed data sets - time
series. This chapter presents a short overview of modern methods of qualitative and
quantitative evaluation of dynamics of complex natural processes such as calculation
of Lyapunov exponents and fractal dimensions, recurrence plots and recurrence
quantification analysis. Other related methods are also described. The traditional
approach to studying dynamical behavior of complex nonlinear systems is to reconstruct from observation scalar time series state or phase space plot. This graph
indicates how the systems behavior changes over the time. We focus on the methods
of identification and quantitative evaluation of complex dynamics that are based
on the testing of evolutionary and geometric properties of phase space graphs as
images of investigated complex dynamics. For practical examples of the application of nonlinear methods for identification of complex natural processes, our results on
medical, geophysical, hydrological, and stick-slip time series analysis are presented.
Key words: complexity, dynamics, nonlinear time series analysis, natural processes.
As nothing in nature is linear I see why you are studying non linear methods. The way I look at everything is from the standpoint of one. Everything is connected to everything. When you single out one I take into account it's relationship to all
