Chemical and Biological Applications of Turing Systems

Part III focuses on spatial instabilities and patterns. We examine the simplest type of spatial pattern in standard reaction-diffusion systems in Chap. 9, namely patterns in a finite domain where the density vanishes at the boundaries. We discuss methods to determine the smallest domain size that supports a nontrivial steady state, known as the critical patch size in ecology. In Chap. 10, we provide first an overview of the Turing instability in standard reaction-diffusion systems. Then we explore how deviations from standard diffusion, namely transport with inertia and anomalous diffusion, affect the Turing instability. Chapter 11 deals with the effects of temporally or spatially varying diffusivities on the Turing instability in reaction-diffusion systems. We present applications of Turing systems to chemical reactions and biological systems in Chap. 12. Chapter 13 deals with spatial instabilities and patterns in spatially discrete systems, such as diffusively and photochemically coupled reactors. 

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