Bifurcations in discontinuous mathematical models with control strategy for a species

Mathematical Biosciences and Engineering

Christian Cortés García¹ 

[1] 1. Department of Mathematics, Universidad Carlos III de Madird, 30 University Avenue, Madrid, Spain 2. Department of Systems Biology, Centro Nacional de Biotecnologia, 3 Darwin Street, Madrid, Spain;

关键词: filippov systems;    pseudo-equilibrium;    growth threshold;    stability;    control parameter;   

DOI  :  10.3934/mbe.2022071

来源: DOAJ

【 摘 要 】

In this paper a preliminary mathematical model is proposed, by means of a system of ordinary differential equations, for the growth of a species. In this case, the species does not interact with another species and is divided into two stages, those that have or have not reached reproductive maturity, with natural and control mortality for both stages. When performing a qualitative analysis to determine conditions in the parameters that allow the extinction or preservation of the species, a modification is made to the model when only control is assumed for each of the stages if the number of species in that stage is above a critical value. These studies are carried out by bifurcation analysis with respect to two parameters: control for each stage and their critical values. It is concluded that for certain conditions in their parameters, the dynamics in each of the controlled stages converge to their critical values.

【 授权许可】

Unknown