MULTIPLE BIFURCATION ANALYSIS AND SPATIOTEMPORAL PATTERNS IN A 1-D GIERER–MEINHARDT MODEL OF MORPHOGENESIS
- 1 April 2010
- journal article
- Published by World Scientific Pub Co Pte Ltd in International Journal of Bifurcation and Chaos
- Vol. 20 (4), 1007-1025
- https://doi.org/10.1142/s0218127410026289
Abstract
A reaction–diffusion Gierer–Meinhardt model of morphogenesis subject to Dirichlet fixed boundary condition in the one-dimensional spatial domain is considered. We perform a detailed Hopf bifurcation analysis and steady state bifurcation analysis to the system. Our results suggest the existence of spatially nonhomogenous periodic orbits and nonconstant positive steady state solutions, which imply the possibility of complex spatiotemporal patterns of the system. Numerical simulations are carried out to support our theoretical analysis.Keywords
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