Dynamical Analysis of a Fractional Order Prey–Predator Model in Crowley–Martin Functional Response with Prey Harvesting †
Abstract
:1. Introduction
2. Model Formulation
3. Existence and Uniqueness of the Solutions
4. Equilibrium Points and Stability Analysis
- (i)
- The trivial equilibrium point is .
- (ii)
- is the boundary equilibrium point.
- (iii)
- is the infected prey free equilibrium point, where ,.
- (iv)
- is the predator free equilibrium point, where ,.
- (v)
- The interior equilibrium point . Where,Now, we want to calculate the Jacobian matrix for a local stability analysis around different equilibrium points. The Jacobian matrix at an arbitrary point is given by, , , ,, , .
5. Numerical Analysis
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Parameters | Biological Representation |
---|---|
L | Susceptible prey |
M | Infected prey |
N | Predator |
Intrinsic prey growth rate | |
K | Carrying capacity of the environment |
Predation rate of susceptible prey | |
Predation rate of infected prey | |
Half-saturation constant | |
c | Conversion coefficient from the prey to predator |
Infected prey death rate | |
Predator population death rate | |
Infection rate |
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Prabhumani, D.N.; Shanmugam, M.; Manickasundaram, S.P.; Thangaraj, N.G. Dynamical Analysis of a Fractional Order Prey–Predator Model in Crowley–Martin Functional Response with Prey Harvesting. Eng. Proc. 2023, 56, 300. https://doi.org/10.3390/ASEC2023-15975
Prabhumani DN, Shanmugam M, Manickasundaram SP, Thangaraj NG. Dynamical Analysis of a Fractional Order Prey–Predator Model in Crowley–Martin Functional Response with Prey Harvesting. Engineering Proceedings. 2023; 56(1):300. https://doi.org/10.3390/ASEC2023-15975
Chicago/Turabian StylePrabhumani, Deepak Nallasamy, Muthukumar Shanmugam, Siva Pradeep Manickasundaram, and Nandha Gopal Thangaraj. 2023. "Dynamical Analysis of a Fractional Order Prey–Predator Model in Crowley–Martin Functional Response with Prey Harvesting" Engineering Proceedings 56, no. 1: 300. https://doi.org/10.3390/ASEC2023-15975