Abstract
Time delay, where it depends on the current state and on the past situation, is often occurred in biological activities, for example, the process by which microorganism consume nutrients into their available biomass is not instantaneous. This investigation inspects the dynamic behavior of stochastic turbidostat model coupled with distributed delay and degenerate diffusion, including sufficient conditions of the extinction and the existence of a unique stationary distribution. What’s more, the existence and uniqueness of globally positive equilibrium of the exploited model are studied. The findings manifest that the turbidostat system is ergodic only when the intensity of white noise is very small. Finally, some numerical examples are proposed to indicate the validity of the theoretical results.
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Acknowledgements
The research is supported by the Natural Science Foundation of China (No. 11871473), Shandong Provincial Natural Science Foundation (Nos. ZR2019MA010, ZR2019MA006, ZR2020MA039) and the Fundamental Research Funds for the Central Universities (No. 19CX02055A).
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DJ designed the research and methodology. XM wrote the original draft. All authors read and approved the final manuscript.
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Mu, X., Jiang, D., Alsaedi, A. et al. A stochastic turbidostat model coupled with distributed delay and degenerate diffusion: dynamics analysis. J. Appl. Math. Comput. 68, 2761–2786 (2022). https://doi.org/10.1007/s12190-021-01639-1
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DOI: https://doi.org/10.1007/s12190-021-01639-1