|
Section
|
Mathematics
|
|
Title
|
Optimal behavior dynamics of the two-species community with intraspecific competition and migration
|
|
Author(-s)
|
Kirillov A.N.a,
Danilova I.V.a
|
|
Affiliations
|
Institute of Applied Mathematical Research, Karelian Research Centre of the Russian Academy of Sciencesa
|
|
Abstract
|
Some problems of the theory of optimal foraging are considered, namely, the problem of predator's choice of the most suitable patch and finding conditions for leaving it. The dynamics of the interaction between the predator and the prey is determined by the Lotka-Volterra system, which takes into account the intraspecific competition of the prey and the possibility of migration of the predator and the prey. Some fractions of populations participate, in the processes of interaction and migration. The problem of finding optimal shares from the point of view of Nash equilibrium is solved. In this case, a partition of the phase space of the system into domains with different behavior of the populations was obtained. We study the optimal trajectories of the corresponding dynamical system with a variable structure, their behavior on the boundaries of the phase space partition. The equilibrium positions are found and their global stability is proved under certain restrictions on the system parameters. In one of the cases of the relationship between the parameters, the study of the qualitative behavior of the optimal trajectories gives rise to the problem of the existence of limit cycles. In this case, an estimate of the corresponding domain of attraction of equilibrium is given.
|
|
Keywords
|
optimal dynamics, intraspecific competition, migration, global stability, Nash equilibrium
|
|
UDC
|
517.977
|
|
MSC
|
37N25
|
|
DOI
|
10.20537/vm190404
|
|
Received
|
5 August 2019
|
|
Language
|
Russian
|
|
Citation
|
Kirillov A.N., Danilova I.V. Optimal behavior dynamics of the two-species community with intraspecific competition and migration, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2019, vol. 29, issue 4, pp. 518-531.
|
|
References
|
- Encyclopedia of animal behavior. Vol. 1, Elsevier, 2019. https://doi.org/10.1016/c2016-1-04542-x
- Kagan E., Ben-Gal I. Search and foraging. Individual motion and swarm dynamics, New York: Chapman and Hall/CRC, 2015. https://doi.org/10.1201/b18604
- Charnov E.L. Optimal foraging, the marginal value theorem, Theoretical Population Biology, 1976, vol. 9, no. 2, pp. 129-136. https://doi.org/10.1016/0040-5809(76)90040-X
- Cressman R., Křivan V. The ideal free distribution as an evolutionarily stable state in density-dependent population games, Oikos, 2010, vol. 119, no. 8, pp. 1231-1242. https://doi.org/10.1111/j.1600-0706.2010.17845.x
- Cressman R., Křivan V. Two-patch population models with adaptive dispersal: the effects of varying dispersal speeds, Journal of Mathematical Biology, 2013, vol. 67, no. 2, pp. 329-358. https://doi.org/10.1007/s00285-012-0548-3
- Matsumura S., Arlinghaus R., Dieckmann U. Foraging on spatially distributed resources with sub-optimal movement, imperfect information, and travelling costs: departures from the ideal free distribution, Oikos, 2010, vol. 119, no. 9, pp. 1469-1483. https://doi.org/10.1111/j.1600-0706.2010.18196.x
- Ivanova A.S., Kirillov A.N. Equilibrium and control in the biocommunity species composition preservation problem, Automation and Remote Control, 2017, vol. 78, no. 8, pp. 1500-1511. https://doi.org/10.1134/S0005117917080100
- Kirillov A.N., Danilova I.V. Dynamics of population patch distribution, Modeling and Analysis of Information Systems, vol. 25, no. 3, pp. 268-275 (in Russian). https://doi.org/10.18255/1818-1015-2018-3-268-275
- Svirezhev Yu.M., Logofet D.O. Ustoichivost' biologicheskikh soobshchestv (Stability of biological communities), Moscow: Nauka, 1978.
- Dey S., Joshi A. Effects of constant immigration on the dynamics and persistence of stable and unstable Drosophila populations, Scientific Reports, 2013, vol. 3, no. 1. https://doi.org/10.1038/srep01405
|
|
Full text
|
|
+7 (3412) 91 60 92
Russian