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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

Editor-in-Chief: Diagana, Toka

Managing Editor: Cánovas, Jose

Mathematical Citation Quotient (MCQ) 2017: 0.71

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Global dynamics and parameter identifiability in a predator-prey interaction model

Jai Prakash Tripathi
  • Department of Mathematics, Central University of Rajasthan, NH-8, Bandarsindri, Kishangarh-305801, Distt.-Ajmer,Rajasthan, India
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Suraj S. Meghwani / Swati Tyagi / Syed Abbas
Published Online: 2018-07-20 | DOI: https://doi.org/10.1515/msds-2018-0009


This paper discusses a predator-prey model with prey refuge. We investigate the role of prey refuge on the existence and stability of the positive equilibrium. The global asymptotic stability of positive interior equilibrium solution is established using suitable Lyapunov functional, which shows that the prey refuge has no influence on the permanence property of the system. Mathematically, we analyze the effect of increase or decrease of prey reserve on the equilibrium states of prey and predator species. To access the usability of proposed predator-prey model in practical scenarios, we also suggest, the use of Levenberg-Marquardt (LM) method for associated parameter estimation problem. Numerical results demonstrate faithful reconstruction of system dynamics by estimated parameter by LM method. The analytical results found in this paper are illustrated with the help of suitable numerical examples

Keywords: Levenberg-Marquardt; Prey refuge; Parameter estimation; Fluctuation Lemma; Lyapunov functional; Permanence


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About the article

Received: 2017-02-26

Accepted: 2018-07-01

Published Online: 2018-07-20

Citation Information: Nonautonomous Dynamical Systems, Volume 5, Issue 1, Pages 113–126, ISSN (Online) 2353-0626, DOI: https://doi.org/10.1515/msds-2018-0009.

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© 2018 Syed Abbas, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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