Dynamical study of quadrating harvesting of a predator–prey model with Monod–Haldane functional response
| Autor: | Rachna Bhatia, Satyaprakash Ahirwar, Reenu Rani, Govinder Nath Verma, Manpreet Kaur |
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| Rok vydání: | 2020 |
| Předmět: |
Equilibrium point
Extinction Applied Mathematics 010102 general mathematics Functional response 01 natural sciences Predation 010101 applied mathematics Computational Mathematics Maximum principle Quadratic equation Bounded function Theory of computation Quantitative Biology::Populations and Evolution Applied mathematics 0101 mathematics Mathematics |
| Zdroj: | Journal of Applied Mathematics and Computing. 66:397-422 |
| ISSN: | 1865-2085 1598-5865 |
| DOI: | 10.1007/s12190-020-01438-0 |
| Popis: | In this study, we have investigated local and global dynamics of a modified Leslie–Gower predator–prey model with Monod–Haldane functional response, where prey is subjected to quadratic harvesting. It is found that the solutions of the proposed system are positive and bounded uniformly. The feasible equilibrium points are also obtained for some suitable and predefined conditions. It is observed that the system exhibits at most three non-zero interior equilibrium points for different choices of parameters under certain conditions. The dynamics of all these feasible equilibrium points have been analysed using Routh–Hurwitz criterion. Local bifurcations analysis such as transcritical and saddle-node bifurcations have been investigated using Sotomayor’s theorem. To demonstrate the analytical results, numerical simulations using some suitable data set are carried out. Optimal harvesting policy has been obtained using Pontryagin’s Maximum Principle to show that the species can be preserved from extinction and a sustainable fishery can be achieved. |
| Databáze: | OpenAIRE |
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