Semi-analytical solutions for the delayed diffusive food-limited model

Abstract

This paper explores how the semi-analytical solutions have been applied on delayed diffusive food-limited models. The Galerkin technique has been used to determine partial differential equations through ordinary differential equations. Steady-state solutions, limit cycles and Hopf bifurcation points are considered. In addition, comparisons between semi-analytical and numerical results show good agreement for steady-state solutions and for the parameter values at which the Hopf bifurcations occur. Example of a stable and unstable limit cycle and Hopf bifurcation points are shown to confirm the results in the Hopf bifurcations map. The benefits and accuracy of the semi-analytical results are confirmed by comparison with the numerical solutions of partial differential equations.