phone +7 (3412) 91 60 92
mail imi@udsu.ru
ru-RU Russian
Home » Issues » Archive of Issues » 2023 - 4 issue » pp. 551-562

Archive of Issues

Russia Rostov-on-Don
Year
2023
Volume
33
Issue
4
Pages
551-562
>>
Section Mathematics
Title Numerical study of the impact of directed migration of non-indigenous species on invasion scenarios
Author(-s) Budyansky A.V.a
Affiliations Don State Technical Universitya
Abstract A mathematical model of competition under conditions of biological invasion, written in the form of a system of nonlinear parabolic equations, is considered. The competition of two closely related species — resident and invader — is studied. The dynamics of populations in a heterogeneous area is determined by local interaction and diffusion. For the invader population, interspecific taxis and directed migration caused by heterogeneity of living conditions are taken into account. In computational experiments, sets of migration parameters corresponding to various invasion scenarios are determined. An analysis of the influence of initial distributions on competitive exclusion and coexistence of species is given.
Keywords math modeling, population dynamics, nonlinear parabolic equations, invasion, taxis
UDC 519.63
MSC 37H25
DOI 10.35634/vm230401
Received 20 October 2023
Language Russian
Citation Budyansky A.V. Numerical study of the impact of directed migration of non-indigenous species on invasion scenarios, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, vol. 33, issue 4, pp. 551-562.
References
  1. Gause G.F. The struggle for existence, Baltimore: The Williams and Wilkins Company, 1934.
  2. Begon M., Harper J.L., Townsend C.R. Ecology. Individuals, populations and communities, Oxford: Blackwell Scientific Publications, 1986.
  3. Murray J.D. Mathematical biology II. Spatial models and biomedical applications, New York: Springer, 2003. https://doi.org/10.1007/b98869
  4. Cantrell R.S., Cosner C. Spatial ecology via reaction–diffusion equations, Chichester: John Wiley and Sons, 2003.
  5. Arumugam Ramesh, Sarkar Sukanta, Banerjee Tanmoy, Sinha Sudipta, Dutta Partha Sharathi. Dynamic environment-induced multistability and critical transition in a metacommunity ecosystem, Physical Review E, 2019, vol. 99, issue 3, 032216. https://doi.org/10.1103/PhysRevE.99.032216
  6. Braverman E., Ilmer I. On the interplay of harvesting and various diffusion strategies for spatially heterogeneous populations, Journal of Theoretical Biology, 2019, vol. 466, pp. 106–118. https://doi.org/10.1016/j.jtbi.2019.01.024
  7. Braverman E., Kamrujjaman Md. Lotka systems with directed dispersal dynamics: Competition and influence of diffusion strategies, Mathematical Biosciences, 2016, vol. 279, pp. 1–12. https://doi.org/10.1016/j.mbs.2016.06.007
  8. Vasilyeva O. Population dynamics in river networks: analysis of steady states, Journal of Mathematical Biology, 2019, vol. 79, pp. 63–100. https://doi.org/10.1007/s00285-019-01350-7
  9. Ge Qing, Tang De. Global dynamics of a two-species Lotka–Volterra competition–diffusion–advection system with general carrying capacities and intrinsic growth rates II: Different diffusion and advection rates, Journal of Differential Equations, 2023, vol. 344, pp. 735–766. https://doi.org/10.1016/j.jde.2022.11.014
  10. Giunta V., Hillen T., Lewis M.A., Potts J.R. Detecting minimum energy states and multi-stability in nonlocal advection–diffusion models for interacting species, Journal of Mathematical Biology, 2022, vol. 85, issue 5, article number: 56. https://doi.org/10.1007/s00285-022-01824-1
  11. Tyutyunov Yu.V., Sen Deeptajyoti, Titova L.I., Banerjee Malay. Predator overcomes the Allee effect due to indirect prey–taxis, Ecological Complexity, 2019, vol. 39, 100772. https://doi.org/10.1016/j.ecocom.2019.100772
  12. Cantrell R.S., Cosner C., Lewis M.A., Lou Yuan. Evolution of dispersal in spatial population models with multiple timescales, Journal of Mathematical Biology, 2020, vol. 80, nos. 1–2, pp. 3–37. https://doi.org/10.1007/s00285-018-1302-2
  13. Budyansky A.V. Impact of directed migration on the occupancy of the area in the «predator–prey» system, Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2020, vol. 17, no. 3, pp. 6–12 (in Russian). https://doi.org/10.31429/vestnik-17-3-6-12
  14. Budyansky A.V., Tsybulin V.G. The effect of directed migration on the formation of spatial population structures, Biophysics, 2015, vol. 60, issue 4, pp. 622–631. https://doi.org/10.1134/S0006350915040077
  15. Budyansky A.V., Frischmuth K., Tsybulin V.G. Cosymmetry approach and mathematical modeling of species coexistence in a heterogeneous habitat, Discrete and Continuous Dynamical Systems — Series B, 2019, vol. 24, issue 2, pp. 547–561. https://doi.org/10.3934/dcdsb.2018196
  16. Frischmuth K., Budyansky A.V., Tsybulin V.G. Modeling of invasion on a heterogeneous habitat: taxis and multistability, Applied Mathematics and Computation, 2021, vol. 410, 126456. https://doi.org/10.1016/j.amc.2021.126456
  17. Yudovich V.I. Cosymmetry, degeneration of solutions of operator equations, and onset of a filtration convection, Mathematical Notes of the Academy of Sciences of the USSR, 1991, vol. 49, issue 5, pp. 540–545. https://doi.org/10.1007/BF01142654
  18. Yudovich V.I. Bifurcations under perturbations violating cosymmetry, Doklady Physics, 2004, vol. 49, issue 9, pp. 522–526. https://doi.org/10.1134/1.1810578
Full text
/doc/issues-2023/23-04-01.pdf
Next article >>