A remark on “Study of a Leslie-Gower-type tritrophic population model”. (English) Zbl 1352.92130
Summary: In [M. A. Aziz-Alaoui, ibid. 14, No. 8, 1275–1293 (2002; Zbl 1031.92027)] a three species ODE model, based on a modified Leslie-Gower scheme is investigated. It is shown that under certain restrictions on the parameter space, the model has bounded solutions for all positive initial conditions, which eventually enter an invariant attracting set. We show that this is not true. To the contrary, solutions to the model can blow up in finite time, even under the restrictions derived in [loc. cit.], if the initial data is large enough. We also prove similar results for the spatially extended system. We validate all of our results via numerical simulations.
MSC:
| 92D25 | Population dynamics (general) |
| 37N25 | Dynamical systems in biology |
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
| 35B44 | Blow-up in context of PDEs |
Citations:
Zbl 1031.92027References:
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