This paper considers semi-analytical solutions for a class of generalised logis- tic partial dierential equations with both point and distributed delays. Both one and two-dimensional geometries are considered. The Galerkin method is used to approximate the governing equations by a system of ordinary dierential delay equations. This method involves assuming a spatial structure for the solution and averaging to obtain the ordinary dierential delay equation models. Semi-analytical results for the stability of the system are derived with the critical parameter value, at which a Hopf bifurcation occurs, found. The results show that diusion acts to stabilise the system, compared to equivalent non- diusive systems and that large delays, which represent feedback from the distant past, act to destabilize the system. Comparisons between semi-analytical and numerical solutions show excellent agreement for steady state and transient solutions, and for the parameter values at which the Hopf bifurcations occur.
History
Citation
Alfifi, H. Y., Marchant, T. R. & Nelson, M. I. (2012). Generalised diffusive delay logistic equations: Semi-analytical solutions. Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, 19 (4-5), 579-596.
Journal title
Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms