Asymptotic Properties of Solutions to Delay Differential Equations Describing Plankton—Fish Interaction
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 a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/23/3064 |
| _version_ | 1797507426734309376 |
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| author | Maria A. Skvortsova |
| author_facet | Maria A. Skvortsova |
| author_sort | Maria A. Skvortsova |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T04:48:19Z |
| format | Article |
| id | doaj.art-5d3714e3f0a04009b9eff4242ad77f9d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T04:48:19Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5d3714e3f0a04009b9eff4242ad77f9d2023-11-23T02:45:29ZengMDPI AGMathematics2227-73902021-11-01923306410.3390/math9233064Asymptotic Properties of Solutions to Delay Differential Equations Describing Plankton—Fish InteractionMaria A. Skvortsova0Laboratory of Differential and Difference Equations, Sobolev Institute of Mathematics, 4, Acad. Koptyug Avenue, 630090 Novosibirsk, RussiaWe 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.https://www.mdpi.com/2227-7390/9/23/3064predator–prey modelplankton–fish interactiondelay differential equationsequilibrium pointasymptotic stabilityestimates for solutions |
| spellingShingle | Maria A. Skvortsova Asymptotic Properties of Solutions to Delay Differential Equations Describing Plankton—Fish Interaction Mathematics predator–prey model plankton–fish interaction delay differential equations equilibrium point asymptotic stability estimates for solutions |
| title | Asymptotic Properties of Solutions to Delay Differential Equations Describing Plankton—Fish Interaction |
| title_full | Asymptotic Properties of Solutions to Delay Differential Equations Describing Plankton—Fish Interaction |
| title_fullStr | Asymptotic Properties of Solutions to Delay Differential Equations Describing Plankton—Fish Interaction |
| title_full_unstemmed | Asymptotic Properties of Solutions to Delay Differential Equations Describing Plankton—Fish Interaction |
| title_short | Asymptotic Properties of Solutions to Delay Differential Equations Describing Plankton—Fish Interaction |
| title_sort | asymptotic properties of solutions to delay differential equations describing plankton fish interaction |
| topic | predator–prey model plankton–fish interaction delay differential equations equilibrium point asymptotic stability estimates for solutions |
| url | https://www.mdpi.com/2227-7390/9/23/3064 |
| work_keys_str_mv | AT mariaaskvortsova asymptoticpropertiesofsolutionstodelaydifferentialequationsdescribingplanktonfishinteraction |