Complex dynamics of a discrete-time predator-prey system with Holling IV functional response |
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| Institution: | 1. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of China;2. State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi 830011, People’s Republic of China;1. Department of Mathematics, University of Azad Jammu & Kashmir, Muzaffarabad 13100, Pakistan;2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, PR China;3. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, PR China;1. Department of Mathematics, BITS Pilani, Pilani Campus, Rajasthan Pilani-333031, India;2. Centre for Ocean, Rivers, Atmosphere and Land Sciences, IIT Kharagpur 721302, India;1. Faculty of Education, Alexandria University, Alexandria, Egypt;2. Faculty of Science, South valley University, Qena, Egypt;3. Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt;1. Department of Mathematical Sciences, College of Science, United Arab Emirats University, Al-Ain, 15551, UAE;2. School of Applied Mathematics, Getulio Vargas Foundation, Rio de Janeiro, RJ 22250-900, Brazil |
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| Abstract: | In this paper, a discrete-time predator-prey system with Holling-IV functional response is studied. We first classify the existence of the fixed points of the system, and further investigate their local stabilities. Then the local bifurcation theory for maps is applied to explore the variety of dynamics of the system. Sufficient conditions for the flip bifurcation and Neimark–Sacker bifurcation are provided. Numerical results demonstrate that the system may have more complex dynamical behaviors including multiple periodic orbits, quasi-periodic orbits and chaotic behavior. The maximum Lyapunov exponent and sensitivity analysis also confirm the chaotic dynamical behaviors of the system. |
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