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Almost periodic solution and global attractivity for a density dependent predator-prey system with mutual interference and Crowley–Martin response function

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Abstract

In this paper, a nonautonomous density dependent predator-prey model with mutual interference and Crowley–Martin response function is proposed and studied. The dynamics of the system is analyzed mainly from the point of view of permanence, extinction, stability, existence and uniqueness of a positive almost periodic solution. It is also shown that the obtained permanence conditions are only sufficient but not necessary. The sufficient conditions are derived for globally attractive unique positive solution by constructing suitable Lyapunov functional. It is shown that sufficient conditions obtained for globally attractive unique positive solution depend on both the predator density dependent death rate and Crowley–Martin coefficient. The obtained analytical results are illustrated with the help of numerical examples.

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Acknowledgments

We are very thankful to the anonymous reviewers and the handling editor for their constructive comments and suggestions which helped us to improve the quality of the paper. This work is fully supported by Central University of Rajasthan, India.

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  1. Department of Mathematics, Central University of Rajasthan NH-8, Bandarsindri, Distt.-Ajmer, 305801, Kishangarh, Rajasthan, India

    Jai Prakash Tripathi

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Tripathi, J.P. Almost periodic solution and global attractivity for a density dependent predator-prey system with mutual interference and Crowley–Martin response function. Differ Equ Dyn Syst 28, 19–37 (2020). https://doi.org/10.1007/s12591-016-0298-6

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