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Instability of equilibria in some delay reaction-diffusion systems

Laister, R.

Authors



Abstract

A new result is derived which extends a known instability result for a class of reaction-diffusion equations to a corresponding system incorporating time delay effects. For a significant class of nonlinear equations it is shown that an unstable equilibrium solution of the reaction-diffusion system cannot be stabilised by the introduction of delay. The result is applied to problems posed on convex domains with homogeneous Neumann boundary conditions. Finally, global methods in bifurcation theory are applied to a delay reaction-diffusion system of Lotka-Volterra type representing the interaction of two mobile species. The existence of a countable set of continua consisting of unstable equilibrium solutions for this system is proved. © 2000 Academic Press.

Journal Article Type Article
Publication Date Jul 15, 2000
Journal Journal of Mathematical Analysis and Applications
Print ISSN 0022-247X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 247
Issue 2
Pages 588-607
APA6 Citation Laister, R. (2000). Instability of equilibria in some delay reaction-diffusion systems. Journal of Mathematical Analysis and Applications, 247(2), 588-607. https://doi.org/10.1006/jmaa.2000.6883
DOI https://doi.org/10.1006/jmaa.2000.6883
Keywords delay reaction-diffusion systems
Publisher URL http://dx.doi.org/10.1006/jmaa.2000.6883