Traveling wave solutions of a diffusive predator–prey model with modified Leslie–Gower and Holling-type II schemes

We study a diffusive predator–prey model with modified Leslie–Gower and Holling-II schemes with D = 0 . We establish the existence of traveling wave solutions connecting a positive equilibrium and a boundary equilibrium via the ‘shooting method’, and the non-existence by the ‘eigenvalue method’. It...

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Bibliographic Details
Published inProceedings of the Indian Academy of Sciences. Mathematical sciences Vol. 128; no. 3; pp. 1 - 18
Main Authors Tian, Yanling, Wu, Chufen
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.06.2018
Springer Nature B.V
Subjects
Eigenvalues
Mathematical models
Mathematics
Mathematics and Statistics
Predator-prey simulation
Traveling waves
Diffusive predator–prey model
traveling wave solution
shooting method
92D25
modified Leslie–Gower
35K57
Holling-type II scheme
35C07
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Summary:We study a diffusive predator–prey model with modified Leslie–Gower and Holling-II schemes with D = 0 . We establish the existence of traveling wave solutions connecting a positive equilibrium and a boundary equilibrium via the ‘shooting method’, and the non-existence by the ‘eigenvalue method’. It should be emphasized that a threshold value c ∗ = 4 α is found in our paper.
ISSN:0253-4142
0973-7685
DOI:10.1007/s12044-018-0401-8