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

  • Yanling Tian
  • Chufen Wu


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 \(c^*=\sqrt{4\alpha }\) is found in our paper.


Diffusive predator–prey model traveling wave solution modified Leslie–Gower Holling-type II scheme shooting method 

2000 Mathematics Subject Classification

35K57 35C07 92D25 



This research is supported by the National Natural Science Foundations of China (11401096) and the Natural Science Foundation of Guangdong Province (2016A030313426), Funds of Guangdong Provincial Engineering Technology Research Center for Data Science (2016KF05) and the research fund of Foshan University.


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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.School of MathematicsSouth China Normal UniversityGuangzhouPeople’s Republic of China
  2. 2.Department of MathematicsFoshan UniversityFoshanPeople’s Republic of China

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