About this book
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.
- DOI https://doi.org/10.1007/978-1-4471-5526-3
- Copyright Information Springer-Verlag London 2014
- Publisher Name Springer, London
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-1-4471-5525-6
- Online ISBN 978-1-4471-5526-3
- Series Print ISSN 0066-5452
- Series Online ISSN 2196-968X
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