Global stability for a new predator–prey model with cross-dispersal among patches based on graph theory
Abstract In this paper, cross-dispersal is considered in a predator–prey model with a patchy environment. A new predator–prey model with cross-dispersal among patches is constructed. A new cross-dispersal matrix is established by the coupling relationship between vertices. First, an existence theore...
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2021
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oai:doaj.org-article:1905b8e318ea457996b927858b76c2cb2021-11-28T12:08:24ZGlobal stability for a new predator–prey model with cross-dispersal among patches based on graph theory10.1186/s13662-021-03645-w1687-1847https://doaj.org/article/1905b8e318ea457996b927858b76c2cb2021-11-01T00:00:00Zhttps://doi.org/10.1186/s13662-021-03645-whttps://doaj.org/toc/1687-1847Abstract In this paper, cross-dispersal is considered in a predator–prey model with a patchy environment. A new predator–prey model with cross-dispersal among patches is constructed. A new cross-dispersal matrix is established by the coupling relationship between vertices. First, an existence theorem of the positive equilibrium for the new model is obtained. Secondly, based on the idea of constructing Lyapunov functions and a graph-theoretical approach for coupled systems, sufficient conditions that the positive equilibrium of the new model is globally asymptotically stable in R + 2 n $R^{2n}_{+}$ are derived on a network with strongly connected graphs. Thirdly, based on the theory of asymptotically autonomous systems, Lyapunov functions method and graph theory, a stability theorem for the positive equilibrium of the new model is established on a complex network without strongly connected graphs. Finally, two examples are given to illustrate main results.Yang GaoSpringerOpenarticleCross-dispersalCoupled modelGlobal stabilityPredator–prey modelPatchesMathematicsQA1-939ENAdvances in Difference Equations, Vol 2021, Iss 1, Pp 1-21 (2021) |
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DOAJ |
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DOAJ |
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EN |
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Cross-dispersal Coupled model Global stability Predator–prey model Patches Mathematics QA1-939 |
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Cross-dispersal Coupled model Global stability Predator–prey model Patches Mathematics QA1-939 Yang Gao Global stability for a new predator–prey model with cross-dispersal among patches based on graph theory |
| description |
Abstract In this paper, cross-dispersal is considered in a predator–prey model with a patchy environment. A new predator–prey model with cross-dispersal among patches is constructed. A new cross-dispersal matrix is established by the coupling relationship between vertices. First, an existence theorem of the positive equilibrium for the new model is obtained. Secondly, based on the idea of constructing Lyapunov functions and a graph-theoretical approach for coupled systems, sufficient conditions that the positive equilibrium of the new model is globally asymptotically stable in R + 2 n $R^{2n}_{+}$ are derived on a network with strongly connected graphs. Thirdly, based on the theory of asymptotically autonomous systems, Lyapunov functions method and graph theory, a stability theorem for the positive equilibrium of the new model is established on a complex network without strongly connected graphs. Finally, two examples are given to illustrate main results. |
| format |
article |
| author |
Yang Gao |
| author_facet |
Yang Gao |
| author_sort |
Yang Gao |
| title |
Global stability for a new predator–prey model with cross-dispersal among patches based on graph theory |
| title_short |
Global stability for a new predator–prey model with cross-dispersal among patches based on graph theory |
| title_full |
Global stability for a new predator–prey model with cross-dispersal among patches based on graph theory |
| title_fullStr |
Global stability for a new predator–prey model with cross-dispersal among patches based on graph theory |
| title_full_unstemmed |
Global stability for a new predator–prey model with cross-dispersal among patches based on graph theory |
| title_sort |
global stability for a new predator–prey model with cross-dispersal among patches based on graph theory |
| publisher |
SpringerOpen |
| publishDate |
2021 |
| url |
https://doaj.org/article/1905b8e318ea457996b927858b76c2cb |
| work_keys_str_mv |
AT yanggao globalstabilityforanewpredatorpreymodelwithcrossdispersalamongpatchesbasedongraphtheory |
| _version_ |
1718408183564730368 |