Reaction-Diffusion Systems with Many Components
We consider some large reaction-diffusion systems which consist of more than two components. We begin with the hypercycle of Eigen and Schuster which has an arbitrary number of components. For this system we determine the maximum number of components for which a stable cluster is possible. Next we study a five-component system for which we will prove the existence and stability of mutually exclusive spikes, i.e. spikes which for different components are located at different positions. Then we consider systems with multiple activators and substrates and derive conditions for stable spiky patterns. Finally, we investigate a consumer chain model, which is a three-component system with two small diffusion constants and prove the existence and stability of a new type of clustered spiky pattern.
- 145.Meinhardt, H.: Models of Biological Pattern Formation. Academic Press, London (1982) Google Scholar
- 236.Volpert, A.I., Volpert, V.A., Volpert, V.A.: Traveling Wave Solutions of Parabolic Systems. Translations of Mathematical Monographs, vol. 140. Am. Math. Soc., Providence (1994) Google Scholar