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Global existence and stability of Nicholson blowflies model with harvesting and random effect

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A Correction to this article was published on 14 March 2022

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Abstract

A generalized Nicholson blowflies model with harvesting or immigration and random effect is considered. We discuss the existence of positive global solution and provide the estimate on the lower bound of the Lyapunov exponent. Moreover, we show that the nontrivial equilibrium solution is mean square exponential stability and stable in probability. We prove several results using techniques of stochastic calculus. It is evident from the obtained conditions that the noise plays an important role in all qualitative properties of the solution. Numerical simulations are also provided in order to validate the analytical findings. The results are new and compliments the existing ones.

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Acknowledgements

We are thankful to the reviewers and editor for their constructive comments and suggestions which helped us to improve the manuscript. The research of M. Niezabitowski was financed by the National Science Centre in Poland granted according to decision DEC-2017/25/B/ST7/02888.

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Authors and Affiliations

  1. School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, 175005, India

    Syed Abbas

  2. Faculty of Automatic Control Electronics and Computer Science, Silesian University of Technology, Akademicka 16, 44-100, Gliwice, Poland

    Michal Niezabitowski

  3. Department of Engineering Mathematics Faculty of Engineering, Ain Shams University, Cairo, Egypt

    Said R. Grace

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  1. Syed Abbas
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  2. Michal Niezabitowski
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  3. Said R. Grace
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Correspondence to Syed Abbas.

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Abbas, S., Niezabitowski, M. & Grace, S.R. Global existence and stability of Nicholson blowflies model with harvesting and random effect. Nonlinear Dyn 103, 2109–2123 (2021). https://doi.org/10.1007/s11071-020-06196-z

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  • DOI: https://doi.org/10.1007/s11071-020-06196-z

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