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Session S39 - Differential Equations and Geometric Structures

Wednesday, July 14, 15:00 ~ 15:50 UTC-3

Dynamics of a pollinator, plant and herbivore populations

Victor Castellanos

Universidad Juárez Autónoma de Tabasco, México   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We carried out the analysis of a three-dimensional ODE nonlinear autonomous system which is derived with the aim of describing the interaction between three populations. These take the form of two mutualistic (pollinators and plants) and a third population (herbivores) is introduced. This one is feeded by consuming plants which, in turn, damages the pollinators population too by reducing the rate of visits (to plants) behalf the pollinators. The specific type of interactions between the populations are described by two types of functional responses of type IV. The main result is the proof of the existence of an attracting limit cycle for the ODE system. This emerges from a supercritical Hopf bifurcation. Its existence is proved by using the Hopf-Andronov bifurcation theorem and its stability is proved by using the first Lyapunov coefficient. In addition of the analysis, a series of numerical simulations are carried out on the full ODE system.

Joint work with Faustino Sánchez-Gardu\~no (Universidad Nacional Autónoma de México, México) and Miguel Angel Dela-Rosa (Universidad Juárez Autónoma de Tabasco-CONACYT, México).

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