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Complex dynamics of an impulsive chemostat model

Complex dynamics of an impulsive chemostat model

Yang, Jin, Tan, Yuanshun and Cheke, Robert A. ORCID: 0000-0002-7437-1934 (2019) Complex dynamics of an impulsive chemostat model. International Journal of Bifurcation and Chaos (ijbc), 29 (8):1950101. ISSN 0218-1274 (Print), 1793-6551 (Online) (doi:https://doi.org/10.1142/S0218127419501013)

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Abstract

We propose a novel impulsive chemostat model with the substrate concentration as the basis for the implementation of control strategies, and then investigate the model’s global dynamics. The exact domains of the impulsive and phase sets are discussed in the light of phase portraits of the model, and then we define the Poincar´e map and study its complex properties. Furthermore, the existence and stability of the microorganism eradication periodic solution are addressed, and the analysis of a transcritical bifurcation reveals that an order-1 periodic solution is generated. We also provide the conditions for the global stability of an order-1 periodic solution and show the existence of order-k (k ≥ 2) periodic solutions. Moreover, the PRCC results and bifurcation analyses not only substantiate our results, but also indicate that the proposed system exists with complex dynamics. Finally, biological implications related to the theoretical results are discussed.

Item Type: Article
Uncontrolled Keywords: impulsive chemostat model, Poincar´e map, order-k periodic solution, transcritical bifurcation, stability
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Engineering & Science
Faculty of Engineering & Science > Natural Resources Institute
Last Modified: 08 Aug 2019 09:14
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/24907

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