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Numerical exploration of the parameter plane in a discrete predator–prey model
Institution:1. Department of Mathematics, School of Natural Sciences, Shiv Nadar University, Post Office Shiv Nadar University, Gautam Buddha Nagar, Greater Noida, Uttar Pradesh 201 314, India;2. Department of Physical and Natural Sciences, School of Liberal Studies, FLAME University, District Pune, Maharashtra 412 115, India;3. Indian Institute of Remote Sensing, Indian Space Research Organization, 4, Kalidas Road, Dehradun, Uttarakhand 248 001, India;4. Jindal School of Art & Architecture, Jindal Global University, Sonipat-Narela Road, Sonipat, Haryana 131 001, India;1. Center for Ecology and Environmental Sciences, Northwestern Polytechnical University, Xi’an 710072, China;2. School of Computer and Information Technology, Shanxi University, Taiyuan 030006, China;3. School of Mechanical Engineering and Center for OPTical IMagery Analysis and Learning (OPTIMAL),Northwestern Polytechnical University, Xi’an 710072, China;1. Protein Research Center, Shahid Beheshti University, G. C., Tehran, Iran;2. Department of Biomedical Engineering, The University of Akron, Akron, OH 44325, USA;1. Institute of Environmental Systems Research, School of Mathematics and Computer Science, Osnabrück University, Osnabrück 49069, Germany;2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2E9, Canada;3. Department of Biological Sciences, University of Alberta,Edmonton, Alberta T6G 2E9, Canada
Abstract:We propose a variant of the discrete Lotka–Volterra model for predator–prey interactions. A detailed stability and numerical analysis of the model are presented to explore the long time behaviour as each of the control parameter is varied independently. We show how the condition for survival of the predator depends on the natural death rate of predator and the efficiency of predation. The model is found to support different dynamical regimes asymptotically including predator extinction, stable fixed point and limit cycle attractors for co-existence of predator and prey and more complex dynamics involving chaotic attractors. We are able to locate exactly the domain of chaos in the parameter plane using a dimensional analysis.
Keywords:Discrete predator–prey model  Bifurcations  Chaos  Dimensional analysis
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