Keywords
nonlinear dynamics, chaos, attractor, modelling, fractal dimension
Start Date
1-7-2008 12:00 AM
Abstract
Temporal behavior of natural phenomena has been difficult to characterize and quantify[Boxian et al. 1994; Broomhead et al. 1986]. Complexity of a natural phenomenon does notdepend on the number of causes that govern it but essentially on the number of theirinterconnections, on the magnitude of such linkages and on the feed-back processes[Drazing, 1992]. An extraordinary advance of the environmental sciences will take place inthe next years as a result the new technologies used in data mining [Sivakumar, 2000;Sivakumar, 2004; Turcotte, 2003]. Specifically, nonlinear analysis it is known that thelong-term behavior of the motion and states of the atmosphere can be described by theglobal attractor. Namely, starting with a given initial value, the solution will tend to theattractor as time goes to infinity. An attractor is a set to which a dynamical system evolvesafter a long enough time. That is, points that get close enough to the attractor remain closeeven if slightly disturbed. The fractal dimension of the atractor in the phase space providesvery useful information about the nature of the processes that generated the sequence ofvalues measured in time [Grassberger P. and I. Procaccia, 1983].
Data Mining vs. Mathematical Modelling: Nonlinear Dynamics and Chaos Theory
Temporal behavior of natural phenomena has been difficult to characterize and quantify[Boxian et al. 1994; Broomhead et al. 1986]. Complexity of a natural phenomenon does notdepend on the number of causes that govern it but essentially on the number of theirinterconnections, on the magnitude of such linkages and on the feed-back processes[Drazing, 1992]. An extraordinary advance of the environmental sciences will take place inthe next years as a result the new technologies used in data mining [Sivakumar, 2000;Sivakumar, 2004; Turcotte, 2003]. Specifically, nonlinear analysis it is known that thelong-term behavior of the motion and states of the atmosphere can be described by theglobal attractor. Namely, starting with a given initial value, the solution will tend to theattractor as time goes to infinity. An attractor is a set to which a dynamical system evolvesafter a long enough time. That is, points that get close enough to the attractor remain closeeven if slightly disturbed. The fractal dimension of the atractor in the phase space providesvery useful information about the nature of the processes that generated the sequence ofvalues measured in time [Grassberger P. and I. Procaccia, 1983].
