Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2007-12-21
Phys. Rev. E 77, R035204 (2008)
Nonlinear Sciences
Pattern Formation and Solitons
4 pages, 3 figures
Scientific paper
10.1103/PhysRevE.77.035204
We study the spatiotemporal properties of coherent states (peaks, holes, and fronts) in a bistable activator-inhibitor system that exhibits biochemical saturated autocatalysis, and in which fronts do not preserve spatial parity symmetry. Using the Gierer-Meinhardt prototype model, we find the conditions in which two distinct pinning regions are formed. The first pinning type is known in the context of variational systems while the second is structurally different due to the presence of a heteroclinic bifurcation between two uniform states. The bifurcation also separates the parameter regions of counterpropagating fronts, leading in turn to the growth or contraction of activator domains. These phenomena expand the range of pattern formation theory and its biomedical applications: activator domain retraction suggests potential therapeutic strategies for patterned pathologies, such as cardiovascular calcification.
Garfinkel Alan
Yochelis Arik
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