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Some Aspects Concerning the Dynamics of Stochastic Chemostats

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Advances in Dynamical Systems and Control

Abstract

In this paper, we study a simple chemostat model influenced by white noise which makes this kind of models more realistic. We use the theory of random attractors and, to that end, we first perform a change of variable using the Ornstein–Uhlenbeck process, transforming our stochastic model into a system of differential equations with random coefficients. After proving that this random system possesses a unique solution for any initial value, we analyze the existence of random attractors. Finally, we illustrate our results with some numerical simulations.

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Acknowledgments

This paper was partially supported by FEDER and Ministerio de Economía y Competitividad under Grant MTM2015-63723-P and Junta de Andalucía under Proyecto de Excelencia P12-FQM-1492. We also would like to thank Alain Rapaport and Stefanie Sonner for the nice discussions that we had with them during the final writing of the paper. Thanks to their helpful suggestions we were able to improve the preliminary version of this paper. Finally, we are really grateful to the referee for the kind comments and useful suggestions which helped us to improve the paper.

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Correspondence to María J. Garrido-Atienza .

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Caraballo, T., Garrido-Atienza, M.J., López-de-la-Cruz, J. (2016). Some Aspects Concerning the Dynamics of Stochastic Chemostats. In: Sadovnichiy, V., Zgurovsky, M. (eds) Advances in Dynamical Systems and Control. Studies in Systems, Decision and Control, vol 69. Springer, Cham. https://doi.org/10.1007/978-3-319-40673-2_11

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  • DOI: https://doi.org/10.1007/978-3-319-40673-2_11

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