Effects of diffusion and advection on predator-prey dynamics in an advective patchy environment. (English) Zbl 07923505
Summary: In this paper, we investigate a specialist predator-prey model within a closed patchy network of streams. Specifically, we focus on the dynamics and asymptotic profiles of positive steady states. Our findings reveal that specialist predators can successfully invade when the mortality rate remains sufficiently low. Additionally, we explore the effects of diffusion and advection on these steady states and the overall species concentration.
MSC:
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 34D23 | Global stability of solutions to ordinary differential equations |
| 37C75 | Stability theory for smooth dynamical systems |
| 92D25 | Population dynamics (general) |
| 92D40 | Ecology |
References:
| [1] | Chen, S.; Liu, J.; Wu, Y., Invasion analysis of a two-species Lotka-Volterra competition model in an advective patchy environment, Stud. Appl. Math., 149, 762-797, 2022 · Zbl 1533.92169 |
| [2] | Chen, S.; Liu, J.; Wu, Y., On the impact of spatial heterogeneity and drift rate in a three-patch two-species Lotka-Volterra competition model over a stream, Z. Angew. Math. Phys., 74, 117, 2023 · Zbl 1519.92187 |
| [3] | Chen, S.; Shi, J.; Shuai, Z.; Wu, Y., Global dynamics of a Lotka-Volterra competition patch model, Nonlinearity, 35, 2, 817-842, 2022 · Zbl 1480.92167 |
| [4] | Ge, Q.; Tang, D., Global dynamics of two-species Lotka-Volterra competition diffusion-advection system with general carrying capacities and intrinsic growth rates, J. Dyn. Differ. Equ., 2022 |
| [5] | Hilker, F. M.; Lewis, M. A., Predator-prey systems in streams and rivers, Theor. Ecol., 3, 175-193, 2010 |
| [6] | Huang, Q.-H.; Jin, Y.; Lewis, M. A., \( R_0\) analysis of a Benthic-drift model for a stream population, SIAM J. Appl. Dyn. Syst., 15, 1, 287-321, 2016 · Zbl 1364.92059 |
| [7] | Jiang, H.; Lam, K.-Y.; Lou, Y., Are two-patch models sufficient? The evolution of dispersal and topology of river network modules, Bull. Math. Biol., 82, 10, Article 131 pp., 2020 · Zbl 1467.34049 |
| [8] | Jiang, H.; Lam, K.-Y.; Lou, Y., Three-patch models for the evolution of dispersal in advective environments: varying drift and network topology, Bull. Math. Biol., 83, 10, Article 109 pp., 2021 · Zbl 1481.34063 |
| [9] | Jin, Y.; Lewis, M. A., Seasonal influences on population spread and persistence in streams: critical domain size, SIAM J. Appl. Math., 71, 4, 1241-1262, 2011 · Zbl 1228.37056 |
| [10] | Lam, K. Y.; Lou, Y.; Lutscher, F., Evolution of dispersal in closed advective environments, J. Biol. Dyn., 9, 1, 188-212, 2015 · Zbl 1448.92378 |
| [11] | Lou, Y.; Lutscher, F., Evolution of dispersal in open advective environments, J. Math. Biol., 69, 6-7, 1319-1342, 2014 · Zbl 1307.35144 |
| [12] | Lou, Y.; Nie, H., Global dynamics of a generalist predator-prey model in open advective environments, J. Math. Biol., 84, 46, 2022 · Zbl 1487.35059 |
| [13] | Lou, Y.; Nie, H.; Wang, Y., Coexistence and bistability of a competition model in open advective environments, Math. Biosci., 306, 10-19, 2018 · Zbl 1409.92267 |
| [14] | Lou, Y.; Xiao, D.-M.; Zhou, P., Qualitative analysis for a Lotka-Volterra competition system in advective homogeneous environment, Discrete Contin. Dyn. Syst., 36, 2, 953-969, 2016 · Zbl 1322.35072 |
| [15] | Lou, Y.; Zhao, X. Q.; Zhou, P., Global dynamics of a Lotka-Volterra competition-diffusion-advection system in advection homogeneous environment, J. Math. Pures Appl., 121, 47-82, 2019 · Zbl 1458.35224 |
| [16] | Lou, Y.; Zhou, P., Evolution of dispersal in advective homogeneous environment: the effect of boundary conditions, J. Differ. Equ., 259, 1, 141-171, 2015 · Zbl 1433.35171 |
| [17] | Lu, Z. Y.; Takeuchi, Y., Global asymptotic behavior in single-species discrete diffusion systems, J. Math. Biol., 32, 1, 67-77, 1993 · Zbl 0799.92014 |
| [18] | Lutscher, F.; Lewis, M. A.; McCauley, E., Effects of heterogeneity on spread and persistence in rivers, Bull. Math. Biol., 68, 8, 2129-2160, 2006 · Zbl 1296.92211 |
| [19] | Lutscher, F.; McCauley, E.; Lewis, M. A., Spatial patterns and coexistence mechanisms in systems with unidirectional flow, Theor. Popul. Biol., 71, 3, 267-277, 2007 · Zbl 1124.92050 |
| [20] | Lutscher, F.; Nisbet, R. M.; Pachepsky, E., Population persistence in the face of advection, Theor. Ecol., 3, 271-284, 2010 |
| [21] | Lutscher, F.; Pachepsky, E.; Lewis, M. A., The effect of dispersal patterns on stream populations, SIAM J. Appl. Math., 65, 1305-1327, 2005 · Zbl 1068.92002 |
| [22] | Ma, L.; Tang, D., Evolution of dispersal in advective homogeneous environments, Discrete Contin. Dyn. Syst., 40, 10, 5815-5830, 2020 · Zbl 1447.35191 |
| [23] | Müller, K., The colonization cycle of freshwater insects, Oecologia, 52, 202-207, 1982 |
| [24] | Nie, H.; Liu, C. R.; Wang, Z. G., Global dynamics of an ecosystem in open advective environments, Int. J. Bifurc. Chaos Appl. Sci. Eng., 31, Article 2150087 pp., 2021 · Zbl 1466.92232 |
| [25] | Nie, H.; Wang, B.; Wu, J. H., Invasion analysis on a predator-prey system in open advective environments, J. Math. Biol., 81, 1429-1463, 2020 · Zbl 1458.35427 |
| [26] | Nie, H.; Xin, S. X.; Shu, H. Y., Effects of diffusion and advection on predator-prey dynamics in closed environments, J. Differ. Equ., 367, 290-331, 2023 · Zbl 1518.92131 |
| [27] | Speirs, D. C.; Gurney, W. S.C., Population persistence in rivers and estuaries, Ecology, 82, 1219-1237, 2001 |
| [28] | Tang, D.; Zhou, P., On a Lotka-Volterra competition-diffusion-advection system: homogeneity vs heterogeneity, J. Differ. Equ., 268, 1570-1599, 2020 · Zbl 1427.35129 |
| [29] | Vasilyeva, O.; Lutscher, F., Population dynamics in rivers: analysis of steady states, Can. Appl. Math. Q., 18, 4, 439-469, 2010 · Zbl 1229.92081 |
| [30] | Vasilyeva, O.; Lutscher, F., How flow speed alters competitive outcome in advective environments, Bull. Math. Biol., 74, 12, 2935-2958, 2012 · Zbl 1362.92091 |
| [31] | Wang, J. F.; Nie, H., Invasion dynamics of a predator-prey system in closed advective environments, J. Differ. Equ., 318, 298-322, 2022 · Zbl 1492.92071 |
| [32] | Wang, M. X., Nonlinear Elliptic Equations, 1990, Science Press |
| [33] | Xin, S.; Li, L.; Nie, H., The effect of advection on a predator-prey model in open advective environments, Commun. Nonlinear Sci. Numer. Simul., 113, Article 106567 pp., 2022 · Zbl 1492.92072 |
| [34] | Yan, X.; Nie, H.; Zhou, P., On a competition-diffusion-advection system from river ecology: mathematical analysis and numerical study, SIAM J. Appl. Dyn. Syst., 21, 1, 438-469, 2022 · Zbl 1484.35034 |
| [35] | Zhou, P.; Xiao, D. M., Global dynamics of a classical Lotka-Volterra competition-diffusion-advection system, J. Funct. Anal., 275, 356-380, 2018 · Zbl 1390.35166 |
| [36] | Zhao, X.-Q.; Zhou, P., On a Lotka-Volterra competition model: the effects of advection and spatial variation, Calc. Var. Partial Differ. Equ., 55, 4, 73, 2016 · Zbl 1366.35088 |
| [37] | Zhou, P., On a Lotka-Volterra competition system: diffusion vs advection, Calc. Var. Partial Differ. Equ., 55, 6, 137, 2016 · Zbl 1377.35160 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
