On the explosive instability in a three‐species food chain model with modified Holling type IV functional response. (3rd May 2017)

• Record Type: Journal Article
• Authors: Parshad, Rana D.; Upadhyay, Ranjit Kumar; Mishra, Swati; Tiwari, Satish Kumar; Sharma, Swarnali
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 16(2017)
• Page Start: 5707
• Page End: 5726
• Publication Date: 2017-05-03
• Subjects: three‐species food chain -- finite‐time blowup -- turing instability -- Hopf bifurcation -- chaos -- time delay; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4419
• Languages: English
• ISSNs: 0170-4214

Abstract

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.