RELAXATION BEHAVIOR AND PATTERN FORMATION IN REACTION-DIFFUSION SYSTEMS

Autor:	Moncho Gomez-Gesteira, Patrick Hanusse, Vicente Pérez-Muñuzuri
Rok vydání:	1994
Předmět:	Field (physics) Oscillation Applied Mathematics Mathematical analysis Rotational symmetry Pattern formation Symmetry (physics) Classical mechanics Modeling and Simulation Reaction–diffusion system Relaxation (approximation) Symmetry breaking Engineering (miscellaneous) Mathematics
Zdroj:	International Journal of Bifurcation and Chaos. :1183-1191
ISSN:	1793-6551 0218-1274
DOI:	10.1142/s0218127494000885
Popis:	The notions of relaxation oscillation and hard excitation have been extensively used and early recognized as important qualitative features of many nonlinear systems. Nevertheless, there seems to exist so far no clear mathematical definitions of these notions. We consider the description of relaxation behavior in oscillating or excitable systems resulting from symmetry breaking of the rotational symmetry of the velocity vector field of the Hopf normal form. From symmetry considerations we detect the first terms responsible for the relaxation character of the phase dynamics in such systems and show that they provide a good general, if not universal, definition of the relaxation properties. We analyze their consequence in the modeling of spatiotemporal patterns such as spiral waves.
Databáze:	OpenAIRE
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