Dynamical analysis for the sustained harvesting of microorganisms using flocculants in a random environment

doi:10.1088/1674-1056/ac9367

中国物理B ›› 2023, Vol. 32 ›› Issue (5): 50502-050502.doi: 10.1088/1674-1056/ac9367

Dynamical analysis for the sustained harvesting of microorganisms using flocculants in a random environment

Rong Liu(刘蓉)^1,2 and Wanbiao Ma(马万彪)^1,†

1 School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;
2 School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

收稿日期:2022-05-04 修回日期:2022-08-24 接受日期:2022-09-21 出版日期:2023-04-21 发布日期:2023-04-26
通讯作者: Wanbiao Ma E-mail:wanbiao_ma@ustb.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11971055) and the Beijing Natural Science Foundation, China (Grant No. 1202019).

Dynamical analysis for the sustained harvesting of microorganisms using flocculants in a random environment

Rong Liu(刘蓉)^1,2 and Wanbiao Ma(马万彪)^1,†

1 School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;
2 School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received:2022-05-04 Revised:2022-08-24 Accepted:2022-09-21 Online:2023-04-21 Published:2023-04-26
Contact: Wanbiao Ma E-mail:wanbiao_ma@ustb.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11971055) and the Beijing Natural Science Foundation, China (Grant No. 1202019).

摘要/Abstract

摘要： The use of flocculants to collect/extract microorganisms is of great practical significance for the development of the application of microorganisms. In this paper, a high-dimensional nonlinear stochastic differential equation model is constructed to describe the continuous culture of microorganisms with multiple nutrients and the flocculation process of microorganisms. The study of the dynamics of this model can provide feasible control strategies for the collection/extraction of microorganisms. The main theoretical results are sufficient conditions for the permanence and extinction of the stochastic differential equation model, which are also extensions of some results in the existing literatures. In addition, through numerical simulations, we vividly demonstrate the statistical characteristics of the stochastic differential equation model.

关键词: stochastic process, stochastically ultimately bounded, stochastic permanence, noise-induced transitions

Abstract: The use of flocculants to collect/extract microorganisms is of great practical significance for the development of the application of microorganisms. In this paper, a high-dimensional nonlinear stochastic differential equation model is constructed to describe the continuous culture of microorganisms with multiple nutrients and the flocculation process of microorganisms. The study of the dynamics of this model can provide feasible control strategies for the collection/extraction of microorganisms. The main theoretical results are sufficient conditions for the permanence and extinction of the stochastic differential equation model, which are also extensions of some results in the existing literatures. In addition, through numerical simulations, we vividly demonstrate the statistical characteristics of the stochastic differential equation model.

Key words: stochastic process, stochastically ultimately bounded, stochastic permanence, noise-induced transitions

中图分类号: (Fluctuation phenomena, random processes, noise, and Brownian motion)

05.40.-a

02.50.-r (Probability theory, stochastic processes, and statistics) 02.50.Ga (Markov processes) 02.50.Ng (Distribution theory and Monte Carlo studies)

Rong Liu(刘蓉) and Wanbiao Ma(马万彪). Dynamical analysis for the sustained harvesting of microorganisms using flocculants in a random environment[J]. 中国物理B, 2023, 32(5): 50502-050502.

Rong Liu(刘蓉) and Wanbiao Ma(马万彪). Dynamical analysis for the sustained harvesting of microorganisms using flocculants in a random environment[J]. Chin. Phys. B, 2023, 32(5): 50502-050502.

参考文献

[1] Ananthi V, Balaji P, Sindhu R, Kim S H, Pugazhendhi A and Arun A 2021 Sci. Total Environ. 780 146467
[2] Wang S K, Stiles A R, Guo C and Liu C Z 2015 Algal Res. 9 178
[3] Li S, Hu T, Xu Y, Wang J, Chu R, Yin Z, Mo F and Zhu L 2020 Renew. Sustain. Energy Rev. 131 110005
[4] Yamada T, Furusawa C, Nagahisa K, Kashiwagi A, Yomo T and Shimizu H 2007 Biosystems 90 614
[5] Tai X, Ma W, Guo S, Yan H and Yin C 2015 Math. Pract. Theory. 45 198 (in Chinese)
[6] Wang W, Ma W and Yan H 2016 Appl. Sci. 6 221
[7] Zhang H and Zhang T 2020 Appl. Math. Lett. 103 106217
[8] Liu R and Ma W 2021 Chaos, Solitons & Fractals 147 110951
[9] Guo S, Cui J A and Ma W 2021 DCDS-B 27 3831
[10] Sikder A and Roy A B 1993 Biosystems 31 39
[11] Jiang D, Shi N and Li X 2008 J. Math. Anal. Appl. 340 588
[12] Li X and Mao X 2009 Discrete Contin Dyn. Syst. 24 523
[13] Liu M, Wang K and Wu Q 2011 Bull Math Biol 73 1969
[14] Lv J, Wang K and Chen D 2015 Methodol Comput Appl Probab 17 403
[15] Xu W, Wang X Y and Liu X Z 2015 Chin. Phys. B 24 050204
[16] Yang J and Wang W 2017 Appl. Math. Lett. 63 59
[17] Wei F and Wang C 2020 Appl. Math. Model. 81 113
[18] Roy J, Barman D and Alam S 2020 Biosystems 197 104176
[19] Li D X and Zhang N 2020 Chin. Phys. B 29 090201
[20] Huo L A, Dong Y F and Lin T T 2021 Chin. Phys. B 30 080201
[21] Xu C, Yu Y, Ren G, Hai X and Lu Z 2021 J. Comput. Nonlinear Dyn. 16 111004
[22] Mao X 2008 Stochastic Differential Equations and Applications 2nd edn. (Chichester: Horwood)
[23] Khasminskii R 2012 Stochastic Stability of Differential Equations (Berlin: Springer)
[24] Wang L, Jiang D and O'Regan D 2016 Commun. Nonlinear Sci. Numer. Simul. 37 1
[25] Zhang Q and Jiang D 2016 J Math Chem 54 777
[26] Wang L and Jiang D 2017 Appl. Math. Lett. 73 22
[27] Doering C R 1986 Phys. Rev. A 34 2564
[28] Wang C J and Mei D C 2008 Chin. Phys. B 17 479
[29] Qin Y H, Luo X S and Wei D Q 2010 Chin. Phys. B 19 050511
[30] Su M B and Rong H W 2011 Chin. Phys. B 20 060501
[31] Gu R C, Xu Y, Zhang H Q and Sun Z K 2011 Acta Phys. Sin. 60 110514 (in Chinese)
[32] Wei Y G, Zeng C H, Wang H, Li K Z and Hu J H 2013 Chin. Phys. B 22 060503
[33] Hailong Z, Enrong W, Fuhong M and Ning Z 2016 Chin. Phys. B 25 030503
[34] Yuan S, Wu D, Lan G and Wang H 2020 Bull Math Biol 82 55
[35] Yang A, Wang H, Zhang T and Yuan S 2022 Chaos 32 043116

Dynamical analysis for the sustained harvesting of microorganisms using flocculants in a random environment

Dynamical analysis for the sustained harvesting of microorganisms using flocculants in a random environment

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Linghongzhi Lu(陆凌弘志), Yang Li(李扬), and Xianbin Liu(刘先斌). Detecting physical laws from data of stochastic dynamical systems perturbed by non-Gaussian α-stable Lévy noise[J]. 中国物理B, 2023, 32(5): 50501-050501.
[2]	Wei-Jing Zhu(朱薇静) and Bao-Quan Ai(艾保全). Ratchet transport of self-propelled chimeras in an asymmetric periodic structure[J]. 中国物理B, 2022, 31(4): 40503-040503.
[3]	Liang'an Huo(霍良安) and Xiaomin Chen(陈晓敏). Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model[J]. 中国物理B, 2022, 31(11): 110204-110204.
[4]	Liang-An Huo(霍良安), Ya-Fang Dong(董雅芳), and Ting-Ting Lin(林婷婷). Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise[J]. 中国物理B, 2021, 30(8): 80201-080201.
[5]	Liang'an Huo(霍良安) and Xiaomin Chen(陈晓敏). Near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters[J]. 中国物理B, 2021, 30(12): 120205-120205.
[6]	朱薇静, 黄小群, 艾保全. Transport of velocity alignment particles in random obstacles[J]. 中国物理B, 2018, 27(8): 80504-080504.
[7]	胡高歌, 高社生, 种永民, 高兵兵. Stochastic stability of the derivative unscented Kalman filter[J]. 中国物理B, 2015, 24(7): 70202-070202.
[8]	王蕊, 孙辉, 马振洋. Stability and performance analysis of a jump linear control system subject to digital upsets[J]. , 2015, 24(4): 40201-040201.
[9]	Ferhat Nutku, Ekrem Aydıner. Current and efficiency of Brownian particles under oscillating forces in entropic barriers[J]. 中国物理B, 2015, 24(4): 40501-040501.
[10]	袁若石, 马易安, 苑波, 敖平. Lyapunov function as potential function：A dynamical equivalence[J]. Chin. Phys. B, 2014, 23(1): 10505-010505.
[11]	覃英华, 罗晓曙, 韦笃取. Random-phase-induced chaos in power systems[J]. 中国物理B, 2010, 19(5): 50511-050511.
[12]	王成玉, 高云, 宋玉敏, 周鹏, 杨海. Stochastic systems with cross-correlated Gaussian white noises[J]. 中国物理B, 2010, 19(11): 116401-116801.
[13]	商朋见, 申金升. Multi-fractal analysis of highway traffic data[J]. 中国物理B, 2007, 16(2): 365-373.
[14]	黄壮雄, 王欣然, 朱涵. Pair correlations in scale-free networks[J]. 中国物理B, 2004, 13(3): 273-278.
[15]	毛晓明, 孙锴, 欧阳颀. Stochastic resonance in a financial model[J]. 中国物理B, 2002, 11(11): 1106-1110.