Nonlinear physics and mechanics

Description of Trajectories of an Evolution Operator Generated by Mosquito Population

Z. S. Boxonov

V. I. Romanovskiy Institute of Mathematics of Uzbek Academy of Sciences Tashkent International University of Financial Management and Technology, University st. 9, Tashkent, 100174 Uzbekistan

Abstract: In this paper, we study discrete-time dynamical systems generated by the evolution operator of mosquito population. An invariant set is found and a Lyapunov function with respect to the operator is constructed in this set. Using the Lyapunov function, the global attraction of a fixed point is proved. Moreover, we give some biological interpretations of our results.

Keywords: Lyapunov function, fixed point, limit point, invariant set

MSC: 39A12, 92D25

Received: 10.11.2023
Accepted: 22.02.2024

Language: English

DOI: 10.20537/nd240401