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Published on: July 30, 2019
Spatio-temporal dynamics of a food chain model featuring Allect effect on prey's growth and sexually reproducing top
1Department of Mathematics, Poornima University, Jaipur, Rajasthan, 303905, India. randhirsng@gmail.com.
Abstract:
This study employs a three-tier food chain framework to examine the influence of the Allee effect on prey foraging efficiency and physiological stability. The model incorporates a Holling type II functional response between the prey and mesopredator, while the top predator is a sexually reproducing species that interacts with the mesopredator through a Crowley-Martin formulation. The system's sensitivity to variations in the half-saturation constant is analyzed to investigate bifurcation phenomena and the onset of chaos. Chaotic behavior is characterized quantitatively using the largest Lyapunov exponent, revealing that changes in the half-saturation constant strongly affect the system's dynamical complexity. To account for spatial processes, the model is extended into a diffusive framework, and the resulting reaction-diffusion system is analyzed for Turing instabilities. Analytical conditions for diffusion-driven instability are derived, and the emergence of spatial patterns is confirmed through numerical simulations. The findings indicate that mutual interference among predators can both destabilize and stabilize the system, depending on parameter values. Increased top predator interference tends to promote stability, whereas enhanced residual decline in predator normalization leads to instability.
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