Semi-analytical solutions for the 1- and 2-D diffusive Nicholson's blowflies equation
Semi-analytical solutions are developed for the diffusive Nicholson's blowflies equation. Both one and two-dimensional geometries are considered. The Galerkin method, which assumes a spatial structure for the solution, is used to approximate the governing delay partial differential equation by a system of ordinary differential delay equations. Both steady-state and transient solutions are presented. Semi-analytical results for the stability of the system are derived and the critical parameter value, at which a Hopf bifurcation occurs, is found. Semi-analytical bifurcation diagrams and phase-plane maps are drawn, which show the initial Hopf bifurcation together with a classical period doubling route to chaos. A comparison of the semi-analytical and numerical solutions shows the accuracy and usefulness of the semi-analytical solutions. Also, an asymptotic analysis for the periodic solution near the Hopf bifurcation point is developed, for the one-dimensional geometry. 2012 The authors 2012. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Please refer to publisher version or contact your library.