Fonseka Nalin and Machado Jonathan and Shivaji Ratnasingham: A study of logistic growth models influenced by the exterior matrix hostility and grazing in an interior patch. (2020)
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Abstract
We will analyze the symmetric positive solutions to the two-point steady state reaction-diffusion equation: −u 00 = u − 1 K u 2 − cu2 1 + u 2 ; x ∈ [L, 1 − L], u − 1 K u 2 ; x ∈ (0, L) ∪ (1 − L, 1), −u 0 (0) + √ λγu(0) = 0, u 0 (1) + √ λγu(1) = 0, where λ, c, K, and γ are positive parameters and the parameter L ∈ (0, 1 2 ). The steady state reaction-diffusion equation above occurs in ecological systems and population dynamics. The above model exhibits logistic growth in the one-dimensional habitat Ω0 = (0, 1), where grazing (type of predation) is occurring on the subregion [L, 1 − L]. In this model, u is the population density and c is the maximum grazing rate. λ is a parameter which influences the equation as well as the boundary conditions, and γ represents the hostility factor of the surrounding matrix. Previous studies have shown the occurrence of S-shaped bifurcation curves for positive solutions for certain parameter ranges when the boundary condition is Dirichlet (γ −→ ∞). Here we discuss the occurrence of S-shaped bifurcation curves for certain parameter ranges, when γ is finite, and their evolutions as γ and L vary.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2020 |
| Number: | 17 |
| ISSN: | 1417-3875 |
| DOI: | 10.14232/ejqtde.2020.1.17 |
| Uncontrolled Keywords: | Differenciálegyenlet, Határérték probléma - differenciálegyenletek |
| Additional Information: | Bibliogr.: 11. p. ; ill. ; összefoglalás angol nyelven |
| Date Deposited: | 2020. Jun. 08. 09:07 |
| Last Modified: | 2021. Oct. 20. 13:52 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/69521 |
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