## DYNAMICAL SYSTEMS Seminar

### On a stochastic logistic growth model with predation and power-type diffusion coefficient: dynamics and optimal harvesting

Susana Pinheiro
()

Abstract: We consider a logistic growth model with a predation term and a stochastic perturbation given by a diffusive term with power-type coefficient. This SDE has the particularity that the standard conditions for the existence and uniqueness of solutions of SDES (linear growth and Lipschitz) do not hold for a large subset of parameter space. Thus, we start by studying the well posedness of the problem at hand, obtaining a detailed characterization for the existence and uniqueness of solutions. We then provide criteria ensuring extinction and persistence of such population. Additionally, we find subsets of parameter space where (absolutely continuous) stationary measures for the SDE under consideration are guaranteed to exist, providing a description for the corresponding densities. We conclude with an initial application to the optimal management of resources. We consider a real asset such as, for instance, a farm or an aquaculture facility, devoted to the exploration of a unique culture or population whose growth follows a SDE such as described above, and look for the optimal harvesting strategy associated with such culture or population.

Monday, January 19, 2015
Time: 15h00
Room: A2-25, Complexo Interdisciplinar, UL
http://cemapre.iseg.ulisboa.pt/seminars/dynsys/