Abstract
In this paper, dynamic behaviors of a turbidostat model with distributed delay are concerned. Hopf bifurcations arise when the value of bifurcation parameter, the time delay of translation for the nutrient, crosses some critical values. Firstly, the type and stability of bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. Moreover, the destabilization of periodic solutions is also discussed. Finally, numerical simulation results are given to support the theoretical conclusions.
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Acknowledgements
We are very grateful to the anonymous referees and the editor for their careful reading of the original manuscript and their kind comments and valuable suggestions that lead to truly significant improvement of the manuscript. This work is supported by the National Natural Science Foundation of China (Grant No. 11561022) and China Postdoctoral Science Foundation (Grant No. 2014M562008).
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Mu, Y., Li, Z., Xiang, H. et al. Bifurcation analysis of a turbidostat model with distributed delay. Nonlinear Dyn 90, 1315–1334 (2017). https://doi.org/10.1007/s11071-017-3728-2
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DOI: https://doi.org/10.1007/s11071-017-3728-2