Perturbations and dynamics of reaction-diffusion systems with mass conservation.
In some reaction-diffusion systems where the total mass of their components is conserved, solutions with initial values near a homogeneous equilibrium converge to a simple localized pattern (spike) after exhibiting Turing-like patterns near the equilibrium for appropriate diffusion coefficients. In this study, we investigate the perturbed reaction-diffusion systems of such conserved systems. We show that a reaction-diffusion model with a globally stable homogeneous equilibrium can exhibit large amplitude Turing-like patterns in the transient dynamics. Moreover, we propose a three-component model, which exhibits an alternating repetition of spatially (almost) homogeneous oscillations and large amplitude Turing-like patterns.
Graduate School of Human Development and Environment, Kobe University, Kobe 657-8501, Japan.
Masataka
M
Kuwamura
Department of Applied Mathematics and Informatics, Ryukoku University, Otsu 520-2194, Japan.
Yoshihisa
Y
Morita
D004058:Diffusion; D008962:Models, Theoretical; D010507:Periodicity