Location of Repository

Spatial distribution of interacting chemical or biological species is usually described by a system of reaction-diffusion equations. In this work we consider a system of two reaction diffusion equations with spatially varying diffusion coefficients which are different for different species and with forcing terms which are the gradient of a spatially varying potential. Such a system describes two competing biological species. We are interested in the possibility of long-term coexistence of the species in a bounded domain. Such long-term coexistence may be associated either with a periodic in time solution (usually associated with a Hopf bifurcation), or with time-independent solutions. We prove that no periodic solution exists for the system. We also consider some steady-states (the time-independent solutions) and examine their stability and bifurcations

Topics:
Partial differential equations

Year: 2007

OAI identifier:
oai:generic.eprints.org:638/core69

Provided by:
Mathematical Institute Eprints Archive

Downloaded from
http://eprints.maths.ox.ac.uk/638/1/paper2NONRWA.pdf

- (1976). Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces,
- (1992). General Problem of the Stability of Motion,
- (1970). Introduction to the theory of stability,
- (1979). Mathematical aspects of reacting and diffusing systems,
- (1984). Maximum principles in differential equations,
- (1986). Minimax methods in critical point theory with applications to differential equations,
- (1989). On the spatial spread of the grey squirrel in
- (1993). Spatial pattern formation for steady states of a population model,
- (1961). Stability by Liapunovâ€™s direct method,
- (1985). Topological methods in bifurcation theory,
- (1964). Topological methods in the theory of nonlinear integral equations,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.