In such a system, successive stages follow each other based on iteration of a certain rule, and which all stages are interacting with each other according to a certain law. Accordingly, deterministic dynamics studies the general features of the entire process. Finally, as an example of dynamical systems approach to studies in economics and finance, I will present the results of some of my recent research in exchange rate modeling which are based on phase space reconstructions of exchange rates dynamics. Landscape ecology offers new concepts, theory and methods that are revealing the importance of spatial patterning on the dynamics of interacting ecosystems. In this talk, I will highlight some insights about landscape pattern and ecological processes that have been derived from simple quantitative models, focusing largely on percolation theory and models derived from cellular automata that simulate dynamics on a gridded landscape.
Percolation theory deals with spatial patterns in randomly assembled systems.
The application of percolation theory to landscape studies has addressed a series of questions dealing with the size, shape and connectivity of habitats as a function of the percentage of a landscape occupied by that habitat type. Because percolation theory generates pattern in the absence of specific processes, the comparison of random maps with actual landscapes provides a neutral model capable of defining the significant departures from randomness of patterned landscapes. This theory has suggested the importance of critical thresholds in connectivity of habitat that, in turn, may influence a variety of ecological processes. Mind-blowing similarities in the way that information is stored, transferred, and used in the respective worlds of silicon and carbon. The mineral zircon preserves the best record of U-Pb age and oxygen isotope composition of magmatic events.