Numerical investigation of pattern dynamics in complex Ginzburg-landau equation

Abstract

Interesting patterns are observed almost everywhere in nature starting from structure of a cell to that of a galaxy. In the area of pattern formation [1], an interesting fact is that similar patterns are observed in a vast variety of systems, giving rise to universalities. There is strong recent research interest [2–10] in finding explanation of the appearance and further evolution of various types of patterns and selection of one pattern over the other. In addition to natural science, it will have applications in many other fields, e.g., economics, population dynamics, etc [11]. A primary aim of studies on pattern formations [1] is to identify the similarities in patterns in apparently different systems and to develop theories for a quantitative understanding for this important and interesting universal phenomena.