Rich Dynamics of a Predator-Prey System with Different Kinds of Functional Responses
In this study, we investigate a mathematical model that describes the interactive dynamics of a predator-prey system with different kinds of response function. The positivity, boundedness, and uniform persistence of the system are established. We investigate the biologically feasible singular points...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/4285294 |
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| author | Kankan Sarkar Subhas Khajanchi Prakash Chandra Mali Juan J. Nieto |
| author_facet | Kankan Sarkar Subhas Khajanchi Prakash Chandra Mali Juan J. Nieto |
| author_sort | Kankan Sarkar |
| collection | DOAJ |
| description | In this study, we investigate a mathematical model that describes the interactive dynamics of a predator-prey system with different kinds of response function. The positivity, boundedness, and uniform persistence of the system are established. We investigate the biologically feasible singular points and their stability analysis. We perform a comparative study by considering different kinds of functional responses, which suggest that the dynamical behavior of the system remains unaltered, but the position of the bifurcation points altered. Our model system undergoes Hopf bifurcation with respect to the growth rate of the prey population, which indicates that a periodic solution occurs around a fixed point. Also, we observed that our predator-prey system experiences transcritical bifurcation for the prey population growth rate. By using normal form theory and center manifold theorem, we investigate the direction and stability of Hopf bifurcation. The biological implications of the analytical and numerical findings are also discussed in this study. |
| format | Article |
| id | doaj-art-4fdc33e126704cac8685126164fb0126 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-4fdc33e126704cac8685126164fb01262025-02-03T06:46:30ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/42852944285294Rich Dynamics of a Predator-Prey System with Different Kinds of Functional ResponsesKankan Sarkar0Subhas Khajanchi1Prakash Chandra Mali2Juan J. Nieto3Department of Mathematics, Malda College, Malda 732101, IndiaDepartment of Mathematics, Presidency University, 86/1 College Street, Kolkata 700073, IndiaDepartment of Mathematics, Jadavpur University, Kolkata 700032, IndiaInstituto de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, SpainIn this study, we investigate a mathematical model that describes the interactive dynamics of a predator-prey system with different kinds of response function. The positivity, boundedness, and uniform persistence of the system are established. We investigate the biologically feasible singular points and their stability analysis. We perform a comparative study by considering different kinds of functional responses, which suggest that the dynamical behavior of the system remains unaltered, but the position of the bifurcation points altered. Our model system undergoes Hopf bifurcation with respect to the growth rate of the prey population, which indicates that a periodic solution occurs around a fixed point. Also, we observed that our predator-prey system experiences transcritical bifurcation for the prey population growth rate. By using normal form theory and center manifold theorem, we investigate the direction and stability of Hopf bifurcation. The biological implications of the analytical and numerical findings are also discussed in this study.http://dx.doi.org/10.1155/2020/4285294 |
| spellingShingle | Kankan Sarkar Subhas Khajanchi Prakash Chandra Mali Juan J. Nieto Rich Dynamics of a Predator-Prey System with Different Kinds of Functional Responses Complexity |
| title | Rich Dynamics of a Predator-Prey System with Different Kinds of Functional Responses |
| title_full | Rich Dynamics of a Predator-Prey System with Different Kinds of Functional Responses |
| title_fullStr | Rich Dynamics of a Predator-Prey System with Different Kinds of Functional Responses |
| title_full_unstemmed | Rich Dynamics of a Predator-Prey System with Different Kinds of Functional Responses |
| title_short | Rich Dynamics of a Predator-Prey System with Different Kinds of Functional Responses |
| title_sort | rich dynamics of a predator prey system with different kinds of functional responses |
| url | http://dx.doi.org/10.1155/2020/4285294 |
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