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Zhu, Huijian; Peng, Yuming; Li, Yiyang; Zeng, Caibin

Forward dynamics and memory effect in a fractional order chemostat minimal model with non-monotonic growth. (English) Zbl 1523.92013

Discrete Contin. Dyn. Syst., Ser. S 16, No. 10, 2749-2764 (2023).
Summary: This paper aims to study the long-time dynamics of chemostat model with non-monotonic growth, subject to random bounded disturbances on the input flow. To be precise, we first prove existence and uniqueness of global positive solution of such model and then construct the compact forward absorbing and attracting sets, which are independent of the realizations of the input noise. Moreover, we prove the conditions for biomass extinction and species persistence. In particular, fractional operator has a noticeable effect, in such a way that it can delay the rate of extinction and persistence and amplitude of oscillator. Numerical simulations are presented to verify the theoretical results.

Cited in 2 Documents

MSC:

92D25 Population dynamics (general)
33E12 Mittag-Leffler functions and generalizations
34A08 Fractional ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models

Keywords:

chemostat model; bounded noise; fractional calculus; non-monotonic growth; Mittag-Leffler function
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References:

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