This monograph is concerned with the mathematical analysis of patterns which are encountered in biological systems. It summarises, expands and relates results obtained in the field during the last fifteen years. It also links the results to biological applications and highlights their relevance to phenomena in nature. Of particular concern are large-amplitude patterns far from equilibrium in biologically relevant models. The approach adopted in the monograph is based on the following paradigms: ac Examine the existence of spiky steady states in reaction-diffusion systems and select as observable patterns only the stable ones ac Begin by exploring spatially homogeneous two-component activator-inhibitor systems in one or two space dimensions ac Extend the studies by considering extra effects or related systems, each motivated by their specific roles in developmental biology, such as spatial inhomogeneities, large reaction rates, altered boundary conditions, saturation terms, convection, many-component systems. Mathematical Aspects of Pattern Formation in Biological Systems will be of interest to graduate students and researchers who are active in reaction-diffusion systems, pattern formation and mathematical biology.For P e A, we use the notation S2 = {y: eye Q}, $22, p = {y: ey + P e Q} and set Pw (y) = Po, w(y), ye Q., p. Our solution will be ... 5.2.1 Technical Analysis In this subsection, we provide some results which will be needed later. We define RN = {(xa#39;anbsp;...

Title | : | Mathematical Aspects of Pattern Formation in Biological Systems |

Author | : | Juncheng Wei, Matthias Winter |

Publisher | : | Springer Science & Business Media - 2013-09-18 |

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