| Abstract: |
| The horse-chestnut leaf miner is a pest that has spread throughout Europe, and controlling its population is a challenge. In a previous study, a non-spatial host-parasitoid model was proposed for controlling the leaf miner, where a generalist parasitoid preys on the leaf miners with a Holling type II functional response. The model identified up to six equilibrium points and discussed their local stability. Here, we revisit the non-spatial model and identify cases that were not explored in the previous investigation. Using a bifurcation theoretical approach, we consider both local stability and global properties of the model. We provide analytical expressions for fold and Hopf bifurcations and the criticality of Hopf bifurcations. Our numerical results reveal interesting dynamics resulting from various bifurcations such as Hopf, fold, transcritical, cyclic-fold, and homoclinic bifurcations of codimension one and Bautin and Bogdanov-Takens bifurcations of codimension two, as well as a Bogdanov-Takens bifurcation of codimension three. Our findings have significant implications for potential pest control strategies. |
|