Impact of cross-diffusion and Allee effect on modified Leslie–Gower model

Sidharth Menon and Sangeeta Kumari

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 236, issue C, 183-199

Abstract: A modified Leslie–Gower model with cross-diffusion and Allee effect is studied. First temporal dynamics of the system is analyzed and the existence of equilibrium points and their corresponding stability analysis are performed. Variation in the Allee effect parameter results in saddle node and Hopf bifurcations. Further, the spatio-temporal model is analyzed and observed that as cross-diffusion gradually increases, prey and predator disperse over the region. Turing instability conditions are derived for cross-diffusion and stability analysis of the amplitude equations is computed to identify the type of the Turing pattern. Analytical conclusions are validated through numerical simulations. As the Allee effect increases, it affects the spatial and temporal dynamics of the prey population. Turing pattern changes from spots to stripes, indicating a large dispersion and a variety of predator interactions, which reduces confinement to secure small areas. In the absence of cross-diffusion, there will be a positive correlation between prey and predator populations. In contrast, when cross-diffusion is present, a negative correlation between prey and predator populations arises.

Keywords: Predator–prey dynamics; Allee effect; Cross-diffusion; Turing patterns; Amplitude equation (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:236:y:2025:i:c:p:183-199

DOI: 10.1016/j.matcom.2025.03.031

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