Topological degree in the generalized gause prey-predator model

We consider a generalized Gause prey-predator model with T-periodic continuous coefficients. In the case where the Poincaré map P over time T is well defined, the result of the paper can be explained as follows: we locate a subset U of R2 such that the topological degree d(I-P,U) equals to +1. The novelty of the paper is that the later is done under only continuity and (some) monotonicity assumptions for the coefficients of the model. A suitable integral operator is used in place of the Poincaré map to cope with possible nonuniqueness of solutions. The paper, therefore, provides a new framework for studying the generalized Gause model with functional differential perturbations and multi-valued ingredients

Integrating identification and qualitative analysis for the dynamic model of a lagoon

This paper deals with the identification and the qualitative analysis of a dynamic model of a shallow lagoon. The model describes the relations between biotic (phytoplankton, zooplankton) and abiotic (oxygen, nutrients) components of a lagoon. The first step of the paper is to derive estimates for the model parameters through an identification procedure using real data. The second step is to perform a qualitative analysis of the model dynamics, via the introduction of a parameterized reduced order model. The main contribution of the paper is to make an effort in the direction of synergyzing the identification stage with the qualitative analysis of the model dynamics, in order to gain a better understanding of the system behavior and obtain more reliable estimates for the model parameters and exogenous inputs