Modeling and Dynamical Analysis of a Beddington–DeAngelis Predator–Prey System With Additional Food and Habitat Complexity

Md. Jasim Uddin, Md. Mutakabbir Khan and Sarker Md. Sohel Rana

International Journal of Mathematics and Mathematical Sciences, 2026, vol. 2026, 1-24

Abstract: Providing predators with additional or alternative food sources, along with increasing habitat complexity, is a widely recognized strategy in biological control. Both theoretical and experimental studies highlight that the quality and quantity of supplementary food are crucial factors influencing the effectiveness of pest regulation. This study reports the dynamics of a predator–prey model employing a Beddington–DeAngelis functional response, with a focus on the synergistic influence of habitat complexity and supplementary food provision. The stability and topological characteristics of the model’s fixed points were determined by deriving specific analytical conditions. These conditions demonstrate that prey refuge exerts a stabilizing influence on the positive fixed point; higher refuge levels enhance stability, whereas lower levels induce instability. Furthermore, bifurcation analysis uncovered that model complexities arise from Neimark–Sacker (NS) and period-doubling (PD) bifurcations, which generate chaotic dynamics. This chaos was verified by positive Lyapunov exponents, displayed across two-parameter bifurcation plots. To detect the presence of chaotic dynamics, we employed the 0–1 test, which confirmed the emergence of irregular, aperiodic behavior within specific parameter regimes. Finally, the Ott–Grebogi–Yorke (OGY) feedback control technique was implemented to suppress the chaotic behavior. Our results demonstrate that nonlinearity and discrete-time dynamics can produce unpredictable population patterns, and we provide precise decisions for achieving ecological stability.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/ijmms/2026/1828568.pdf (application/pdf)
http://downloads.hindawi.com/journals/ijmms/2026/1828568.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:1828568

DOI: 10.1155/ijmm/1828568

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().