Dynamics of a Predator-Prey Population in the Presence of Resource Subsidy under the Influence of Nonlinear Prey Refuge and Fear Effect
In this work, our aim is to investigate the impact of a non-Kolmogorov predator-prey-subsidy model incorporating nonlinear prey refuge and the effect of fear with Holling type II functional response. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (...
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| Published in | Complexity (New York, N.Y.) Vol. 2021; no. 1 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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2021
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| Abstract | In this work, our aim is to investigate the impact of a non-Kolmogorov predator-prey-subsidy model incorporating nonlinear prey refuge and the effect of fear with Holling type II functional response. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). The positivity and asymptotically uniform boundedness of the solutions of the system have been derived. Analytically, we have studied the criteria for the feasibility and stability of different equilibrium points. In addition, we have derived sufficient conditions for the existence of local bifurcations of codimension 1 (transcritical and Hopf bifurcation). It is also observed that there is some time lag between the time of perceiving predator signals through vocal cues and the reduction of prey’s birth rate. So, we have analyzed the dynamical behaviour of the delayed predator-prey-subsidy model. Numerical computations have been performed using MATLAB to validate all the analytical findings. Numerically, it has been observed that the predator, prey, and subsidy can always exist at a nonzero subsidy input rate. But, at a high subsidy input rate, the prey population cannot persist and the predator population has a huge growth due to the availability of food sources. |
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| AbstractList | In this work, our aim is to investigate the impact of a non-Kolmogorov predator-prey-subsidy model incorporating nonlinear prey refuge and the effect of fear with Holling type II functional response. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). The positivity and asymptotically uniform boundedness of the solutions of the system have been derived. Analytically, we have studied the criteria for the feasibility and stability of different equilibrium points. In addition, we have derived sufficient conditions for the existence of local bifurcations of codimension 1 (transcritical and Hopf bifurcation). It is also observed that there is some time lag between the time of perceiving predator signals through vocal cues and the reduction of prey’s birth rate. So, we have analyzed the dynamical behaviour of the delayed predator-prey-subsidy model. Numerical computations have been performed using MATLAB to validate all the analytical findings. Numerically, it has been observed that the predator, prey, and subsidy can always exist at a nonzero subsidy input rate. But, at a high subsidy input rate, the prey population cannot persist and the predator population has a huge growth due to the availability of food sources. |
| Author | Mondal, Sudeshna Nieto, Juan J. Samanta, G. P. |
| Author_xml | – sequence: 1 givenname: Sudeshna orcidid: 0000-0001-8300-1591 surname: Mondal fullname: Mondal, Sudeshna organization: Department of MathematicsIndian Institute of Engineering Science and TechnologyShibpurHowrah 711103Indiaiiests.ac.in – sequence: 2 givenname: G. P. orcidid: 0000-0002-2956-6265 surname: Samanta fullname: Samanta, G. P. organization: Department of MathematicsIndian Institute of Engineering Science and TechnologyShibpurHowrah 711103Indiaiiests.ac.in – sequence: 3 givenname: Juan J. orcidid: 0000-0001-8202-6578 surname: Nieto fullname: Nieto, Juan J. organization: Instituto de MatemáticasUniversidade de Santiago de CompostelaSantiago de Compostela 15782Spainusc.es |
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| Copyright | Copyright © 2021 Sudeshna Mondal et al. Copyright © 2021 Sudeshna Mondal et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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| SubjectTerms | Animal behavior Biomass Birth rate Ecosystems Endangered & extinct species Fear Food Foxes Hopf bifurcation Influence Mathematical models Mortality Population Predation Predators Stability analysis Subsidies Time lag Wolves |
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| Title | Dynamics of a Predator-Prey Population in the Presence of Resource Subsidy under the Influence of Nonlinear Prey Refuge and Fear Effect |
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