Asymptotic Properties of Solutions to Delay Differential Equations Describing Plankton—Fish Interaction

Maria A Skvortsova

doi:10.3390/math9233064

Abstract

We consider a system of differential equations with two delays describing plankton–fish interaction. We analyze the case when the equilibrium point of this system corresponding to the presence of only phytoplankton and the absence of zooplankton and fish is asymptotically stable. In this case, the asymptotic behavior of solutions to the system is studied. We establish estimates of solutions characterizing the stabilization rate at infinity to the considered equilibrium point. The results are obtained using Lyapunov–Krasovskii functionals.

Highlights

There exist a large number of works devoted to the study of biological models described by delay differential equations (see, for example, the monographs [1,2,3,4]and bibliography therein)
At present, there exist a large number of works devoted to the study of biological models described by delay differential equations
Taking into account a model proposed in [14], in the present paper, we study the model of the following form:

Summary

Introduction

There exist a large number of works devoted to the study of biological models described by delay differential equations (see, for example, the monographs [1,2,3,4]and bibliography therein). The aim of the present paper is, under condition (3), to establish estimates for all components of the solution to the initial value problems (1) and (2) characterizing the stabilization rate at infinity to equilibrium point (K, 0, 0)T .

Objectives

Results

Conclusion