On the explosive instability in a three‐species food chain model with modified Holling type IV functional response |
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Authors: | Rana D Parshad Ranjit Kumar Upadhyay Swati Mishra Satish Kumar Tiwari Swarnali Sharma |
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Institution: | 1. Department of Mathematics, Clarkson University, Potsdam, USA;2. Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad 826004, India;3. Department of Mathematics, Bengal Engineering and Science University Shibpur, India |
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Abstract: | In earlier literature, a version of a classical three‐species food chain model, with modified Holling type IV functional response, is proposed. Results on the global boundedness of solutions to the model system under certain parametric restrictions are derived, and chaotic dynamics is shown. We prove that in fact the model possesses explosive instability, and solutions can explode/blow up in finite time, for certain initial conditions, even under the parametric restrictions of the literature. Furthermore, we derive the Hopf bifurcation criterion, route to chaos, and Turing bifurcation in case of the spatially explicit model. Lastly, we propose, analyze, and simulate a version of the model, incorporating gestation effect, via an appropriate time delay. The delayed model is shown to possess globally bounded solutions, for any initial condition. Copyright © 2017 John Wiley & Sons, Ltd. |
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Keywords: | three‐species food chain finite‐time blowup turing instability Hopf bifurcation chaos time delay |
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