BLOW UP IN FINITE TIME OF SOLUTIONS TO A LESLIE-GOWER PREDATOR-PREY
MODEL IN ABSCENCE OF THE MIDDLE PREDATOR.
Abstract
In order to study the asymptotic behavior, several authors claimed
global existence in time of solutions to a tritrophic food chain models
following a modied Leslie-Gower formulation considering the interactions
between three species: a generalist top predator depredating on a middle
predator, that in turn is depreds a prey. To the contrary it is shown
nite time blow-up in such models can occur. We show in this work that
blow up in nite time persists even when the intermediate (middle)
predator is abscent to the contrary to what it is claimed by Kundu and
Patra (2022, [13]). It is shown under some restrictions on the
parameters, the model has bounded solutions for all positive initial
conditions. We show that this is not true. Solutions to the model can
blow up in nite time, for initial data suciently large, even under the
restrictions derived by the authors. We can show same results even for
small initial data but we concentrate our proofs for the rst case. We
also show similar results for the spatially extended system. We
illustrate all our results through numerical simulations.