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

Author

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  • Maria A. Skvortsova

    (Laboratory of Differential and Difference Equations, Sobolev Institute of Mathematics, 4, Acad. Koptyug Avenue, 630090 Novosibirsk, Russia)

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.

Suggested Citation

  • Maria A. Skvortsova, 2021. "Asymptotic Properties of Solutions to Delay Differential Equations Describing Plankton—Fish Interaction," Mathematics, MDPI, vol. 9(23), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3064-:d:690240
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