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| Bifurcation of a Modified Leslie-Gower Systemwith Discrete and Distributed Del |
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| KeyWord:Modified Leslie-Gower system discrete and distributed delays stability Hopf bifurcation. |
| Author Name | Affiliation | | Zhongkai Guo | College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou, Gansu 730050, China | | Haifeng Huo | College of Electrical and Information Engineering, Lanzhou University of
Technology, Lanzhou, Gansu 730050, China
Department of Applied Mathematics, Lanzhou University of Technology,
Lanzhou, Gansu 730050, China | | Qiuyan Ren | College of Electrical and Information Engineering, Lanzhou University of
Technology, Lanzhou, Gansu 730050, China | | Hong Xiang | Department of Applied Mathematics, Lanzhou University of Technology,
Lanzhou, Gansu 730050, China |
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| Abstract: |
| A modified Leslie-Gower predator-prey system with discrete and distributed delays is introduced. By analyzing the associated characteristic equation, stability and local Hopf bifurcation of the model are studied. It is found that the positive equilibrium is asymptotically stable when $\tau$ is less than a critical value and unstable when $\tau$ is greater than this critical value and the system can also undergo Hopf bifurcation at the positive equilibrium when $\tau$ crosses this critical value. Furthermore, using the normal form theory and center manifold theorem, the formulae for determining the direction of periodic solutions bifurcating from positive equilibrium are derived. Some numerical simulations are also carried out to illustrate our results. |
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