Gradient Pattern Analysis of  Swift-Hohenberg Dynamics

Abstract: Spatially extended nonlinear dynamical systems are rich in the structures and patterns that arise from its time evolution. In this paper we analyze a problem that has received less attention: the pattern formation characterization in a non-uniformly forced system. The study is based on the numerical integration of the Swift-Hohenberg equation and adresses the characterization of symmetry breaking and phase disorder detected from gradient computational operators as Amplitude Asymmetric Fragmentation  and Complex Entropic Form. The main result shows that these operators are useful in characterizing the formation of small defects due mainly from phase dynamics. The transition from amplitude to phase dynamics domain is also well characterized numerically by means of these gradient field operators.