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Noise-induced control of environmental fluctuations in a three-species predator–prey model

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Abstract

A three-species ecological model is proposed that comprises one prey and two predators (low predator and top predator) to understand the persistence and/or extinction of prey and predators under a suitable environment. The realistic ecological system is typically inhomogeneous in terms of spatiotemporal variations of population density. With this motivation, white noise is introduced to the system to conceive the impact of environmental heterogeneity on the interaction of prey and predators. The boundedness of solutions of the system is presented. The condition for the local stability of the deterministic model is established. The stochastic analysis of the system suggests the impression of the environmental noise on the dynamical behaviour of solutions. Numerical results reveal that the proposed system exhibits an oscillatory pattern of solutions. It is shown that the white noise in the low predator has a dominating role in comparison with other noises to keep the oscillation in order. Moreover, to investigate the spatial dependency of the population density, diffusion term is introduced to the system that also displays oscillatory behaviour of the solutions. The results also confirm that the population density of prey, low predator, and top predator have a biological control in the oscillatory behaviour. In the presence of diffusion and white noise, numerical simulation illustrates the sensitivity of the diffusion coefficients and the amplitude of noises. Numerical results lead to a reasonable agreement with the analytical findings in both non-spatial and spatial systems.

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Acknowledgement

The authors are sincerely thankful to the anonymous referees for their insightful comments that helped to enhance the quality of the article.

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Authors and Affiliations

  1. Department of Basic and Applied Sciences, National Institute of Food Technology Entrepreneurship and Management, Kundli, Haryana, 131 028, India

    Kalyan Das

  2. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632 014, India

    M. N. Srinivash

  3. Department of Mathematics, Jahangirnagar University, Dhaka, 1342, Bangladesh

    M. Humayun Kabir & M. Osman Gani

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  1. Kalyan Das
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  2. M. N. Srinivash
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  3. M. Humayun Kabir
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  4. M. Osman Gani
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Correspondence to M. Humayun Kabir.

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Das, K., Srinivash, M.N., Kabir, M.H. et al. Noise-induced control of environmental fluctuations in a three-species predator–prey model. Model. Earth Syst. Environ. 7, 2675–2695 (2021). https://doi.org/10.1007/s40808-020-01051-x

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