A discrete-time dynamical system and an evolution algebra of mosquito population

TL;DR

This paper introduces a discrete-time dynamical system for mosquito populations using an evolution algebra, analyzes its fixed points, and explores algebraic properties with biological implications.

Contribution

It develops a novel discrete-time model based on evolution algebras for mosquito populations and analyzes its fixed points and algebraic structure.

Findings

The system has two saddle fixed points under certain conditions.

An evolution algebra is constructed from the Jacobian at fixed points.

Biological interpretations of algebraic properties are provided.

Abstract

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.