2018/03/05 by U. A. Rozikov, Rozikov, U. A., María V. Velasco +1
Mathematics · Medicine · #92D25 (34C60 34D20 92D30 92D40) #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.1803.01503
openalex publication_date 2018/03/05 · openalex created_date 2018/03/29 · openalex updated_date 2026/07/28
Recently, continuous-time dynamical systems, based on systems of ordinary differential equations, for mosquito populations are studied. In this paper we consider discrete-time dynamical system generated by an evolution quadratic operator of mosquito population and show that this system has two fixed points, which are saddle points (under some conditions on the parameters of the system). We construct an evolution algebra taking its matrix of structural constants equal to the Jacobian of the quadratic operator at a fixed point. Idempotent and absolute nilpotent elements, simplicity properties and some limit points of the evolution operator corresponding to the evolution algebra are studied. We give some biological interpretations of our results.