Some results on predator-prey and competitive population dynamics

Mathematical analysis is a useful tool to give insights in very different mathematical biology problems.

In this talk we will consider predator-prey and competition population dynamics models. We will give an overview of recent results in the case of seasonally forced models not entering in technical details.

First of all we consider predator-prey models with or without Allee effect and prove results on extinction or persistence. We will give some examples such as models including competition among predators, prey-mesopredator-superpredator models and Leslie-Gower systems. When Allee effect is considered, we deal with the cases of strong and weak Allee effect.

Then we consider competition models of two species giving conditions for the extinction of one or both species and for coexistence.

This talk is based in joint works with I. Coelho, M. Garrione, C. Soresina and E. Sovrano.

References:

[1] I. Coelho and C. Rebelo, Extinction or coexistence in periodic Kolmogorov systems of competitive type, submitted.

[2] M. Garrione and C. Rebelo, Persistence in seasonally varying predator-prey systems via the basic reproduction number, Nonlinear Analysis: Real World Applications, 30, (2016) 73-98.

[3] C. Rebelo and C. Soresina, Coexistence in seasonally varying predator-prey systems with Allee effect, Nonlinear Anal. Real World Appl. 55 (2020), 103140, 21 pp.