Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 65, Issue 11, Pages 1727-1737Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2013.04.004
Keywords
Diffusive system; Modified Leslie-Gower; Positive steady states; Permanence
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Funding
- Natural Science Foundation of China [10831005, 11102041, 11201072]
- Natural Science Foundation of Fujian Province [2011J01002, 2012J01002]
- Foundation of Fujian Education Bureau [JB12030]
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The diffusive predator-prey system with modified Leslie-Gower and Holling-type III schemes is considered here. Firstly, stability analysis of the equilibrium for a reduced ODE system is discussed. Secondly, we obtain that the system is permanent. Thirdly, sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the system are derived by using the method of Lyapunov function. Finally, we establish the existence and nonexistence of nonconstant positive steady states of this reaction-diffusion system, which indicates the effect of large diffusivity. (c) 2013 Elsevier Ltd. All rights reserved.
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