Modeling of retention effects in dispersion processes of the invasive species

Abstract

This article addresses a dynamic population problem, with a description of the front of waves that represent the invasion of the studied species – Tucunaré (Cichla Ocelaris). The study propos-es a new model for the invasion process, whereas the invasive species maintains, temporarily, a fraction of the total population in the conquered territory; in order establish a self-sustaining population. In this case, the spatial distribution of this species, cannot be represented only by Fick’s Law (classical diffu-sion), since there’s a new phenomenon involved in the process, that cannot be characterized merely by manipulating the parameters of diffusivity. Thus, we evaluate a new model, which explicitly includes the temporary retention processes through of inclusion of a fourth-order term. The dynamic population problem considered, it describes the wave’s front propagating that represent the invasion of the studied species, and it is modeled, i.e., mathematically by transport equations that are resolved numerically, with the application of finite element methods.