| Citation: |
Changjin Xu, Ercan Balci. HUNTING COOPERATION AND GESTATION DELAY IN A PREY-PREDATOR MODEL WITH FRACTIONAL DERIVATIVE[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 1035-1053. doi: 10.11948/20250147
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HUNTING COOPERATION AND GESTATION DELAY IN A PREY-PREDATOR MODEL WITH FRACTIONAL DERIVATIVE
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Abstract
Predator-prey dynamics are central to ecological modeling, with the Lotka-Volterra framework serving as a foundational tool for studying these interactions. In this study, we propose a novel fractional-order predator-prey model incorporating cooperative hunting and gestation delays to better capture the complexities of real-world ecosystems. The cooperative hunting mechanism enhances predator efficiency, while gestation delay accounts for the time required for biomass transfer from prey to predator reproduction. Additionally, we integrate fractional derivatives to introduce memory effects, allowing the system to retain past influences on population dynamics. We establish the dynamical analysis of the model. Through numerical simulations, we demonstrate the interplay between cooperation, delay, and memory effects, revealing rich dynamical behaviors.
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References
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Changjin Xu, Ercan Balci. HUNTING COOPERATION AND GESTATION DELAY IN A PREY-PREDATOR MODEL WITH FRACTIONAL DERIVATIVE[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 1035-1053. doi: 10.11948/20250147
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Figure 1.
Prey (blue) and predator (red) populations with respect to time where the fractional order
$ \alpha=1 $ $ \alpha=0.85 $ $ \tau=0 $ $ \tau=0.20 $ $ \tau=0.33 $ -
Figure 2.
Time-series solutions and corresponding phase diagrams.
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Figure 3.
Time-series solutions and corresponding phase diagrams.
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Figure 4.
Time-series solutions where the fractional order
$ \alpha=1 $ $ \alpha=0.85 $ $ \tau=0 $ $ \tau=0.20 $ $ \tau=0.25 $ -
Figure 5.
Time-series solutions and corresponding phase diagrams.
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Figure 6.
Time-series solutions of the system (3.1) for different initial conditions where
$ \sigma=3, \, \kappa=0.8, \, \beta=1.5, \, \tau=0.09, \, \alpha=0.85 . $ -
Figure 7.
Time-series solutions and corresponding phase diagrams for different values of hunting cooperation parameter
$ \beta $ $ \tau=0.25, \, \alpha=0.85 $