Spatial dynamics and pattern formation in fragmented habitats: A study using a diffusive Bazykin model with Allee effect

Pallav Jyoti Pal, Debabrata Biswas and Tapan Saha

Chaos, Solitons & Fractals, 2025, vol. 192, issue C

Abstract: This article explores the dynamics of a Bazykin-type prey–predator model enhanced with an additive Allee effect in the prey population growth. The model reveals complex dynamics, such as bistability, global asymptotic stability, and a variety of local and global bifurcations, including saddle–node, Hopf, Bogdanov–Takens, transcritical, cusp, homoclinic, Generalized-Hopf, and saddle–node bifurcations of limit cycles (SNLC). By varying two key parameters, the parametric space is partitioned into ten distinct subregions, wherein the study provides an in-depth understanding of the behaviour of the system within each region. The influence of both strong and weak Allee effects on system dynamics is discussed, particularly focusing on the potential for total extinction of both populations under a strong Allee effect. Quantitative analysis and necessary numerical simulations validate the analytical findings and demonstrate the applicability of the temporal model. In addition, the evolution of stationary and non-stationary patterns is explored in a fragmented habitat with a Z-like structure, which presents greater challenges for numerical simulations due to its complex boundaries. The simulations reveal how the geometry of the fragmented habitats influence spatiotemporal pattern formation, emphasizing the impact of domain geometry on transient patterns and their duration. Analytical conditions are derived to guarantee the existence of stationary patterns, and extensive numerical simulations are performed to investigate the effect of the spatial domain structure on pattern formation.

Keywords: Bazykin model; Pattern formation; Allee effect; Fragmented habitats; Bifurcation; Bistability (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077925000566

DOI: 10.1016/j.chaos.2025.116043

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