Domain Structured Dynamics

Complex dynamics provides the mathematical tools to help us study chaos, revealing irregularity within these very sensitive systems. As fractals, stochastic processes, neural networks, and differential equations, with their intricate analysis, applications for industry, and potentials within theoretical and real world research have an indisputably close relationship with chaos, it is aimed to unite these subjects in this book.

Domain structured dynamics introduces a new method for analysis of chaos in fractals, neural networks and random processes. It starts with newly invented abstract similarity sets and maps, which are in the basis of the abstract similarity dynamics. They are realized in the domain structured dynamics by a carefully designed labeling procedure. The analysis is similar to that one by symbolic dynamics, but it is

much more efficient with potential to become universal in the future. The results are in the stream of Pythagorean doctrine, considering finite number of indices for the labeling. In this book, one can see the immediate power of the approach for fractals as domains of chaos, revisited famous deterministic and stochastic models, new types of differential equations and neural networks.