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Role of multiple time delays on a stage-structured predator–prey system in a toxic environment

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  • Santra, Nirapada
  • Saha, Sangeeta
  • Samanta, Guruprasad

Abstract

In this paper, a stage-structured predator–prey model is considered in a toxic environment, emphasizing on the affect of the toxic substances on growth of the species in presence of time delays. The positivity and boundedness of solutions have been discussed. The analytical and numerical simulations of the proposed model show that the coexistence equilibrium point is stable for low and moderate values of the delay parameter associated with the predator’s maturity. Even though there is an interval of the maturation time in which the system exhibits oscillatory behaviour, a longer maturity duration may lead to the extinction of the predator species. The impact of toxicity on the proposed system is also investigated. The stability of the system repeatedly switches as the time delay, related to the changes of toxicity incurred in the adult predator, varies, and finally becomes unstable for a significant value of it. Besides that, the delay related to the prey’s toxicity has also led some exciting results.

Suggested Citation

  • Santra, Nirapada & Saha, Sangeeta & Samanta, Guruprasad, 2023. "Role of multiple time delays on a stage-structured predator–prey system in a toxic environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 548-583.
    • Handle: RePEc:eee:matcom:v:212:y:2023:i:c:p:548-583
    DOI: 10.1016/j.matcom.2023.05.015
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    References listed on IDEAS

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    1. Nirapada Santra & Sudeshna Mondal & Guruprasad Samanta, 2022. "Complex Dynamics of a Predator–Prey Interaction with Fear Effect in Deterministic and Fluctuating Environments," Mathematics, MDPI, vol. 10(20), pages 1-38, October.
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