Dynamics of a Leslie–Gower Holling-type II predator–prey system with Lévy jumps |
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| Institution: | 1. Department of Mathematics, China University of Petroleum (East China), Qingdao 266580, PR China;2. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, King Abdulaziz University;1. Department of Mathematics, Central University of Rajasthan NH-8, Bandarsindri, Kishangarh-305801, Distt.-Ajmer, Rajasthan, India;2. School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, 175001, H.P., India;1. School of Mathematical Science, Huaiyin Normal University, Huaian 223300, PR China;2. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, PR China |
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| Abstract: | This paper is concerned with a stochastic predator–prey system with modified Leslie–Gower and Holling-type II schemes with Lévy jumps. First, we prove there is a unique positive solution to the system with a positive initial value. Then we establish the sufficient conditions for stability in mean and extinction of the system. Finally, we introduce some numerical simulations to support the main results. The results shows that the Lévy jumps can change the properties of the population systems significantly. |
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| Keywords: | Predator–prey model Lévy noise Stability in mean Extinction |
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