Effect of Toxicant on One Prey and Two Competing Predators with Beddington-DeAngelis Functional Response

Kavita Makwana, Raveendra Babu A., B.P.S. Jadon

Abstract


This study investigates the dynamical behaviour of a prey-predator system with two competing predators, incorporating the Beddington–DeAngelis functional response and the effects of environmental toxicants. Analytical analysis ensures the boundedness of solutions, guaranteeing biologically feasible population dynamics. Equilibrium points are identified, and their stability is examined using local and global stability analyses. Numerical simulations validate the analytical findings, demonstrating that as the competition coefficient b1 increases, the system transitions from a stable equilibrium to periodic oscillations and eventually to chaotic behaviour. Furthermore, the impact of the toxicant uptake rate d1 is explored to assess its role in system stability. The results indicate that low levels of toxicant absorption promote oscillatory dynamics, while higher values of d1 suppress population growth and restore stability. This highlights the dual role of toxicants in ecological systems, where moderate exposure disrupts equilibrium, but excessive accumulation can lead to stabilization. Bifurcation diagrams and time-series simulations further reinforce these transitions, revealing critical thresholds where stability is lost or regained. The study provides valuable insights into the complex interplay between toxicant dynamics, predator-prey interactions, and bifurcation phenomena. The findings emphasize the ecological implications of toxicant exposure and interspecies competition, offering potential applications in environmental management and conservation strategies.


Keywords


Mathematical modelling; Stability analysis; Bifurcation; Sensitivity analysis; Parameter variation.

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DOI: https://doi.org/10.37905/jjbm.v6i1.30686

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