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Differential equations --- Differential equations, Parabolic --- Équations différentielles paraboliques --- Reaction-diffusion equations. --- Équations de réaction-diffusion --- Asymptotic theory. --- Théorie asymptotique --- Reaction-diffusion equations --- Asymptotic theory of parabolic differential equations --- Asymptotic expansions --- Diffusion-reaction equations --- Equations, Reaction-diffusion --- Asymptotic theory --- Équations de réaction-diffusion. --- Théorie asymptotique.

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Mathematical physics --- Reaction-diffusion equations. --- Perturbation (Mathematics) --- Eigenvalues. --- Équations de réaction-diffusion --- Perturbation (mathématiques) --- Valeurs propres --- Eigenvalues --- Reaction-diffusion equations --- Diffusion-reaction equations --- Equations, Reaction-diffusion --- Differential equations, Parabolic --- Perturbation equations --- Perturbation theory --- Approximation theory --- Dynamics --- Functional analysis --- Matrices --- Équations de réaction-diffusion. --- Valeurs propres.

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This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception, parts of the book can also be used in master’s level mathematical biology courses.

Mathematics. --- Partial differential equations. --- Biomathematics. --- Mathematical physics. --- Mathematical and Computational Biology. --- Partial Differential Equations. --- Mathematical Physics. --- Biology --- Mathematics --- Partial differential equations --- Physical mathematics --- Physics --- Math --- Science --- Differential equations, partial. --- Reaction-diffusion equations. --- Diffusion-reaction equations --- Equations, Reaction-diffusion --- Differential equations, Parabolic

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Numerical solutions of algebraic equations --- Numerical solutions of differential equations --- 519.61 --- Error analysis (Mathematics) --- Numerical calculations --- Reaction-diffusion equations --- Diffusion-reaction equations --- Equations, Reaction-diffusion --- Differential equations, Parabolic --- Numerical analysis --- Errors, Theory of --- Instrumental variables (Statistics) --- Mathematical statistics --- Statistics --- Numerical methods of algebra --- Numerical calculations. --- Reaction-diffusion equations. --- Error analysis (Mathematics). --- 519.61 Numerical methods of algebra --- Équations de réaction-diffusion --- Calculs numériques --- Calcul d'erreur --- Équations de réaction-diffusion. --- Calculs numériques. --- Calcul d'erreur.

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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: • Examine the existence of spiky steady states in reaction-diffusion systems and select as observable patterns only the stable ones • Begin by exploring spatially homogeneous two-component activator-inhibitor systems in one or two space dimensions • 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.

Pattern formation (Biology) --- Reaction-diffusion equations. --- Diffusion-reaction equations --- Equations, Reaction-diffusion --- Biological pattern formation --- Mathematics. --- Partial differential equations. --- Biomathematics. --- Partial Differential Equations. --- Mathematical and Computational Biology. --- Genetics and Population Dynamics. --- Physiological, Cellular and Medical Topics. --- Biology --- Mathematics --- Partial differential equations --- Math --- Science --- Differential equations, Parabolic --- Developmental biology --- Differential equations, partial. --- Genetics --- Physiology --- Animal physiology --- Animals --- Anatomy --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Biological systems --- Mathematical models.