Global Dynamics of a Discrete Mosquito Model with Allee Effect

TL;DR

This paper studies the complex behavior of a two-dimensional discrete mosquito population model with an Allee effect, analyzing stability and dynamics through theoretical and numerical methods.

Contribution

It provides a comprehensive analysis of the model's dynamics, including stability and fixed points, with validation via numerical examples.

Findings

Existence of positive invariant trajectories

Identification of fixed points and their stability

Numerical validation of theoretical results

Abstract

In this paper, we investigate the dynamical behavior of a two-dimensional discrete mosquito model incorporating an Allee effect. We analyze the system's trajectory comprehensively, examining both local and global dynamics. Our analysis begins by establishing the invariance of the positive trajectory within the first quadrant. We then investigate the existence of fixed points within this region. Following this, we perform a stability analysis to determine both local and global asymptotic stability of the identified fixed points. Finally, we validate the effectiveness and applicability of our theoretical results through numerical examples.