Analysis of Stochastic Predator-Prey Model with Disease in the Prey and Holling Type II Functional Response
A stochastic predator-prey model with disease in the prey and Holling type II functional response is proposed and its dynamics is analyzed. We discuss the boundedness of the dynamical system and find all feasible equilibrium solutions. For the stochastic systems, we obtain the conditions for the exi...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/3632091 |
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| author | C. Gokila M. Sambath K. Balachandran Yong-Ki Ma |
| author_facet | C. Gokila M. Sambath K. Balachandran Yong-Ki Ma |
| author_sort | C. Gokila |
| collection | DOAJ |
| description | A stochastic predator-prey model with disease in the prey and Holling type II functional response is proposed and its dynamics is analyzed. We discuss the boundedness of the dynamical system and find all feasible equilibrium solutions. For the stochastic systems, we obtain the conditions for the existence of the global unique solution, boundedness, and uniform continuity. We derive the conditions for extinction and permanence of species. Moreover, we construct appropriate Lyapunov functions and discuss the asymptotic stability of equilibria. To illustrate our theoretical findings, we have performed numerical simulations and presented the results. |
| format | Article |
| id | doaj-art-ddba56ee35064c72888de15fb011b92c |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-ddba56ee35064c72888de15fb011b92c2025-02-03T05:49:39ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/36320913632091Analysis of Stochastic Predator-Prey Model with Disease in the Prey and Holling Type II Functional ResponseC. Gokila0M. Sambath1K. Balachandran2Yong-Ki Ma3Department of Mathematics, Periyar University, Salem 636 011, IndiaDepartment of Mathematics, Periyar University, Salem 636 011, IndiaDepartment of Mathematics, Bharathiar University, Coimbatore 641 046, IndiaDepartment of Applied Mathematics, Kongju National University, Chungcheongnam-do 32588, Republic of KoreaA stochastic predator-prey model with disease in the prey and Holling type II functional response is proposed and its dynamics is analyzed. We discuss the boundedness of the dynamical system and find all feasible equilibrium solutions. For the stochastic systems, we obtain the conditions for the existence of the global unique solution, boundedness, and uniform continuity. We derive the conditions for extinction and permanence of species. Moreover, we construct appropriate Lyapunov functions and discuss the asymptotic stability of equilibria. To illustrate our theoretical findings, we have performed numerical simulations and presented the results.http://dx.doi.org/10.1155/2020/3632091 |
| spellingShingle | C. Gokila M. Sambath K. Balachandran Yong-Ki Ma Analysis of Stochastic Predator-Prey Model with Disease in the Prey and Holling Type II Functional Response Advances in Mathematical Physics |
| title | Analysis of Stochastic Predator-Prey Model with Disease in the Prey and Holling Type II Functional Response |
| title_full | Analysis of Stochastic Predator-Prey Model with Disease in the Prey and Holling Type II Functional Response |
| title_fullStr | Analysis of Stochastic Predator-Prey Model with Disease in the Prey and Holling Type II Functional Response |
| title_full_unstemmed | Analysis of Stochastic Predator-Prey Model with Disease in the Prey and Holling Type II Functional Response |
| title_short | Analysis of Stochastic Predator-Prey Model with Disease in the Prey and Holling Type II Functional Response |
| title_sort | analysis of stochastic predator prey model with disease in the prey and holling type ii functional response |
| url | http://dx.doi.org/10.1155/2020/3632091 |
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