Extinctions in a Metapopulation with Nonlinear Dispersal Coupling
Abstract
:1. Introduction
2. Materials and Methods
3. Two-Patch System
4. Multi-Patch System
4.1. Existence and Uniqueness, Steady-State Points
4.2. Solutions as a Monotone Dynamical System
5. Computer Simulations
6. Discussion and Concluding Remarks
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Case No. | Model | q | Which | p | ||
---|---|---|---|---|---|---|
1 | Quadratic | 20 | 7Q | 6.0829 | 2.7824 | 0.5180 |
2 | Quadratic | 20 | 8Q | 6.3336 | 2.9024 | 0.5287 |
3 | Quadratic | 20 | 9Q | 6.1039 | 2.7939 | 0.5161 |
4 | Linear | 5 | 1 | 5.9931 | 2.7475 | 0.4981 |
5 | Linear | 20 | 1 | 5.9931 | 2.7475 | 0.4981 |
6 | Linear | 5 | 5 | 6.1951 | 3.2314 | −0.2678 |
7 | Linear | 20 | 5 | 6.1951 | 3.2314 | −0.2678 |
8 | Linear | 5 | 6L | 5.8518 | 2.9176 | 0.0166 |
9 | Linear | 20 | 6L | 5.8518 | 2.9176 | 0.0166 |
10 | Linear | 5 | 9L | 5.9594 | 2.9715 | 0.0163 |
11 | Linear | 20 | 9L | 5.9594 | 2.9715 | 0.0163 |
12 | Linear | 20 | 10L | 6.1707 | 3.0772 | 0.0162 |
13 | Linear | 20 | 11L | 5.9465 | 2.9655 | 0.0155 |
14 | Linear | 5 | 13L | 5.9663 | 2.9750 | 0.0163 |
15 | Linear | 20 | 13L | 5.9663 | 2.9750 | 0.0163 |
16 | Linear | 5 | 14L | 5.7967 | 2.8902 | 0.0164 |
17 | Linear | 20 | 14L | 5.7967 | 2.8902 | 0.0164 |
18 | Linear | 20 | 15L | 5.8942 | 2.9389 | 0.0165 |
19 | Linear | 5 | 17L | 6.1019 | 3.0428 | 0.0163 |
20 | Linear | 20 | 17L | 6.1019 | 3.0428 | 0.0163 |
Case No. | Model | q | Which | p | ||
---|---|---|---|---|---|---|
21 | Quadratic | 5 | 1 | 5.9931 | 2.7475 | 0.4981 |
22 | Quadratic | 11.5 | 1 | 5.9931 | 2.7475 | 0.4981 |
23 (NI) | Quadratic | 1.5 | 2 | 5.8322 | 3.2905 | −0.7489 |
24 (NI) | Quadratic | 0.5 | 3 | 5.9883 | 3.0180 | −0.0477 |
25 (NI) | Quadratic | 1 | 3 | 5.9883 | 3.0180 | −0.0477 |
26 (NI) | Quadratic | 3.5 | 4 | 6.4793 | 3.2230 | 0.0333 |
27 | Quadratic | 0.5 | 5 | 6.1951 | 3.2314 | −0.2678 |
28 | Quadratic | 4.5 | 5 | 6.1951 | 3.2314 | −0.2678 |
29 | Quadratic | 4.5 | 6Q | 6.0280 | 2.7574 | 0.5132 |
30 | Quadratic | 7.5 | 10Q | 6.0660 | 2.7756 | 0.5147 |
31 | Linear | 9.5 | 2 | 5.8322 | 3.2905 | −0.7489 |
32 | Linear | 5 | 3 | 5.9883 | 3.0180 | −0.0477 |
33 | Linear | 5 | 4 | 6.4792 | 3.2230 | 0.0333 |
34 | Linear | 13 | 4 | 6.4792 | 3.2230 | 0.0333 |
35 (NI) | Linear | 13 | 7L | 5.4677 | 2.7261 | 0.0156 |
36 | Linear | 10 | 8L | 5.9101 | 2.9469 | 0.0163 |
37 | Linear | 12 | 8L | 5.9101 | 2.9469 | 0.0163 |
38 (NI) | Linear | 8.5 | 12L | 5.9783 | 2.9812 | 0.0159 |
39 | Linear | 5 | 16L | 5.6687 | 2.8261 | 0.0164 |
40 | Linear | 11 | 16L | 5.6687 | 2.8261 | 0.0164 |
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Korotkov, A.; Petrovskii, S. Extinctions in a Metapopulation with Nonlinear Dispersal Coupling. Mathematics 2023, 11, 4337. https://doi.org/10.3390/math11204337
Korotkov A, Petrovskii S. Extinctions in a Metapopulation with Nonlinear Dispersal Coupling. Mathematics. 2023; 11(20):4337. https://doi.org/10.3390/math11204337
Chicago/Turabian StyleKorotkov, Alexander, and Sergei Petrovskii. 2023. "Extinctions in a Metapopulation with Nonlinear Dispersal Coupling" Mathematics 11, no. 20: 4337. https://doi.org/10.3390/math11204337