Effect of fear in a fractional order prey–predator model with time delayed carrying capacity
The Caputo technique is used in this article to analyze the fractional-order predator–prey scenario. Incorporating a delayed carrying capacity for the prey population and posing the impact of individual prey fear on predators are two aspects of this. We first provide the model’s formulation in terms...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-06-01
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| Series: | Results in Control and Optimization |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666720725000530 |
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| author | Pramodh Bharati Subrata Paul Animesh Mahata Supriya Mukherjee Subhabrata Mondal Banamali Roy |
| author_facet | Pramodh Bharati Subrata Paul Animesh Mahata Supriya Mukherjee Subhabrata Mondal Banamali Roy |
| author_sort | Pramodh Bharati |
| collection | DOAJ |
| description | The Caputo technique is used in this article to analyze the fractional-order predator–prey scenario. Incorporating a delayed carrying capacity for the prey population and posing the impact of individual prey fear on predators are two aspects of this. We first provide the model’s formulation in terms of an integer order derivative, and subsequently we expand it to a fractional order system in terms of the Caputo derivative. The article contains a number of conclusions about the prerequisites for the model’s existence and uniqueness as well as the restrictions on the boundedness and positivity of the solution. To satisfy the requirements for the existence and uniqueness of the precise solution, the Lipschitz condition is applied. Within the local context, we have examined the stability of equilibrium points. Additionally, we investigated whether Hopf bifurcation may occur at the interior equilibrium point of our suggested model. We have used the Generalised Euler technique to approximatively solve the model. The suggested scheme’s dependability is indicated by the fact that the results produced using the current numerical approach converge to equilibrium for the fractional order. For our research, MATLAB was used to enable graphical representations and numerical simulations. |
| format | Article |
| id | doaj-art-9e5ba5ea3bc64932af212679227a9307 |
| institution | Kabale University |
| issn | 2666-7207 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Control and Optimization |
| spelling | doaj-art-9e5ba5ea3bc64932af212679227a93072025-08-20T03:31:10ZengElsevierResults in Control and Optimization2666-72072025-06-011910056710.1016/j.rico.2025.100567Effect of fear in a fractional order prey–predator model with time delayed carrying capacityPramodh Bharati0Subrata Paul1Animesh Mahata2Supriya Mukherjee3Subhabrata Mondal4Banamali Roy5Department of Mathematics, Ramnagar College, Depal, Purba Medinipur 721453, West Bengal, India; Department of Mathematics, Swami Vivekananda University, Barrackpore Rd, Bara Kanthalia, West Bengal 700121, IndiaDepartment of Mathematics, Arambagh Govt. Polytechnic, Arambagh 712602, West Bengal, IndiaDepartment of Mathematics, Sri Ramkrishna Sarada Vidya Mahapitha, Kamarpukur, Hooghly 712612, India; Corresponding author.Department of Mathematics, Gurudas College, 1/1 Suren Sarkar Road, Kolkata 700054, West Bengal, IndiaDepartment of Mathematics, Swami Vivekananda University, Barrackpore Rd, Bara Kanthalia, West Bengal 700121, IndiaDepartment of Mathematics, Bangabasi Evening College, 19 Rajkumar Chakraborty Sarani, Kolkata 700009, West Bengal, IndiaThe Caputo technique is used in this article to analyze the fractional-order predator–prey scenario. Incorporating a delayed carrying capacity for the prey population and posing the impact of individual prey fear on predators are two aspects of this. We first provide the model’s formulation in terms of an integer order derivative, and subsequently we expand it to a fractional order system in terms of the Caputo derivative. The article contains a number of conclusions about the prerequisites for the model’s existence and uniqueness as well as the restrictions on the boundedness and positivity of the solution. To satisfy the requirements for the existence and uniqueness of the precise solution, the Lipschitz condition is applied. Within the local context, we have examined the stability of equilibrium points. Additionally, we investigated whether Hopf bifurcation may occur at the interior equilibrium point of our suggested model. We have used the Generalised Euler technique to approximatively solve the model. The suggested scheme’s dependability is indicated by the fact that the results produced using the current numerical approach converge to equilibrium for the fractional order. For our research, MATLAB was used to enable graphical representations and numerical simulations.http://www.sciencedirect.com/science/article/pii/S2666720725000530Time lagStabilityHopf bifurcationGeneralized Euler schemeNumerical study |
| spellingShingle | Pramodh Bharati Subrata Paul Animesh Mahata Supriya Mukherjee Subhabrata Mondal Banamali Roy Effect of fear in a fractional order prey–predator model with time delayed carrying capacity Results in Control and Optimization Time lag Stability Hopf bifurcation Generalized Euler scheme Numerical study |
| title | Effect of fear in a fractional order prey–predator model with time delayed carrying capacity |
| title_full | Effect of fear in a fractional order prey–predator model with time delayed carrying capacity |
| title_fullStr | Effect of fear in a fractional order prey–predator model with time delayed carrying capacity |
| title_full_unstemmed | Effect of fear in a fractional order prey–predator model with time delayed carrying capacity |
| title_short | Effect of fear in a fractional order prey–predator model with time delayed carrying capacity |
| title_sort | effect of fear in a fractional order prey predator model with time delayed carrying capacity |
| topic | Time lag Stability Hopf bifurcation Generalized Euler scheme Numerical study |
| url | http://www.sciencedirect.com/science/article/pii/S2666720725000530 |
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