Global dynamics and parameter identifiability in a predator-prey interaction model
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 tha...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-07-01
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| Series: | Nonautonomous Dynamical Systems |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/msds.2018.5.issue-1/msds-2018-0009/msds-2018-0009.xml?format=INT |
| _version_ | 1818701041414176768 |
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| author | Tripathi Jai Prakash Meghwani Suraj S. Tyagi Swati Abbas Syed |
| author_facet | Tripathi Jai Prakash Meghwani Suraj S. Tyagi Swati Abbas Syed |
| author_sort | Tripathi Jai Prakash |
| collection | DOAJ |
| description | 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 |
| first_indexed | 2024-12-17T15:14:32Z |
| format | Article |
| id | doaj.art-08c2046f734947079a254a69085d796d |
| institution | Directory Open Access Journal |
| issn | 2353-0626 |
| language | English |
| last_indexed | 2024-12-17T15:14:32Z |
| publishDate | 2018-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonautonomous Dynamical Systems |
| spelling | doaj.art-08c2046f734947079a254a69085d796d2022-12-21T21:43:33ZengDe GruyterNonautonomous Dynamical Systems2353-06262018-07-015111312610.1515/msds-2018-0009msds-2018-0009Global dynamics and parameter identifiability in a predator-prey interaction modelTripathi Jai Prakash0Meghwani Suraj S.1Tyagi Swati2Abbas Syed3Department of Mathematics, Central University of Rajasthan, NH-8, Bandarsindri, Kishangarh-305801, Distt.-Ajmer,Rajasthan, IndiaSchool of Basic Sciences, Indian Institute of Technology Mandi,Mandi, 175001, H.P., IndiaSchool of Basic Sciences, Indian Institute of Technology Mandi,Mandi, 175001, H.P., IndiaSchool of Basic Sciences, Indian Institute of Technology Mandi,Mandi, 175001, H.P., IndiaThis 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 exampleshttp://www.degruyter.com/view/j/msds.2018.5.issue-1/msds-2018-0009/msds-2018-0009.xml?format=INTLevenberg-MarquardtPrey refugeParameter estimationFluctuation LemmaLyapunov functionalPermanence |
| spellingShingle | Tripathi Jai Prakash Meghwani Suraj S. Tyagi Swati Abbas Syed Global dynamics and parameter identifiability in a predator-prey interaction model Nonautonomous Dynamical Systems Levenberg-Marquardt Prey refuge Parameter estimation Fluctuation Lemma Lyapunov functional Permanence |
| title | Global dynamics and parameter identifiability in a predator-prey interaction model |
| title_full | Global dynamics and parameter identifiability in a predator-prey interaction model |
| title_fullStr | Global dynamics and parameter identifiability in a predator-prey interaction model |
| title_full_unstemmed | Global dynamics and parameter identifiability in a predator-prey interaction model |
| title_short | Global dynamics and parameter identifiability in a predator-prey interaction model |
| title_sort | global dynamics and parameter identifiability in a predator prey interaction model |
| topic | Levenberg-Marquardt Prey refuge Parameter estimation Fluctuation Lemma Lyapunov functional Permanence |
| url | http://www.degruyter.com/view/j/msds.2018.5.issue-1/msds-2018-0009/msds-2018-0009.xml?format=INT |
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