Dynamical analysis of a prey-predator model incorporating a prey refuge with variable carrying capacity |
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| Affiliation: | 1. Department of Mathematics, Sultan Qaboos University, Al-Khoudh 123, Oman;2. Center of Preparatory Studies, Sultan Qaboos University, Al-Khoudh 123, Oman;3. School of IT Information and Control Engineering, Kunsan National University, Gunsan 54150, South Korea;1. School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, Shanxi 030006, China;2. School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China;1. Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, Villeurbanne 69622, France;2. INRIA Team Dracula, INRIA Lyon La Doua, Villeurbanne 69603, France;3. Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, Russian Federation;4. Department of Mathematics & Statistics, IIT Kanpur, Kanpur 208016, India;5. Department of Mathematics, Vijaygarh Jyotish Ray College, Kolkata 700032, India;1. Department of Mathematical Sciences, Shahrekord University, Shahrekord, Iran;2. Department of Applied Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou 215123, China;3. Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Porto, Portugal |
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| Abstract: | A prey-predator model incorporating prey refuge with variable carrying capacity and Holling type-II functional response is proposed and analyzed. The model includes a case of increasing carrying capacity as well as a decreasing carrying capacity case. Sufficient conditions are derived to ensure the existence and local stability of the equilibrium points of the proposed model. Moreover, the occurrence of transcritical bifurcation as well as Hopf bifurcation are investigated. The effect of some model parameter related to the prey refuge and the variable carrying capacity on the prey-predator dynamics has been examined. Numerical simulations are presented to demonstrate the theoretical results and to illustrate the effect of these parameters on the model dynamics. Moreover, a comparison with the constant carrying case has been presented. |
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