参考文献/References:
［1］ 陈兰荪, 陈键. 非线性生物动力系统［M］. 北京: 科学出版社, 1993.
Chen Lansun, Chen Jian. Nonlinear biology dynamics［M］. Beijing：Science Press, 1993.(in Chinese)
［2］ Smith H L, Waltman P. Theory of the Chemostat［M］. Cambridge(UK): Cambridge University Press, 1995.
［3］ Williams F M. Dynamics of microbial populations, systems analysis and simulation in Ecology［M］. Cambridge,USA: Academic Press, 1971.
［4］ Xu Chaoqun, Yuan Sanling, Zhang Tonghua. Asymptotic behavior of a Chemostat model with stochastic perturbation on the dilution rate［J］. Abstract & Applied Analysis, 2013(1): 233-242.
［5］ Imhof L, Walcher S. Exclusion and persistence in deterministic and stochastic chemostat models［J］. Journal of Differential Equations, 2005, 217(1): 26-53.
［6］ 李相龙, 许超群, 原三领. 一类随机环境中恒化器模型的动力学行为分析［J］. 生物数学学报, 2015, 30(1): 181-191.
Li Xianglong, Xu Chaoqun, Yuan Sanling. Analysis on the dynamics behavior of a chemostat model in stochastic environment［J］. Journal of Biomathematics, 2015, 30(1): 181-191.(in Chinese)
［7］ 董庆来. 具有比率型功能反应函数的随机恒化器系统的渐近性态［J］. 山东大学学报理学版, 2014, 49(3): 68-72.
Dong Qinglai. Asymptotic behavior of a stochastic ratio-dependent chemostat model［J］. Journal of Shandong University Natural Science, 2014,49(3): 68-72.(in Chinese)
［8］ Chen Zhenzhen, Zhang Tonghua. Dynamics of a stochastic model for continuous flow bioreactor with Contois growth rate［J］. Journal of Mathematical Chemistry, 2013, 51(3): 1076-1091.
［9］ 付桂芳, 马万彪. 由微分方程所描述的微生物连续培养动力系统(I)［J］. 微生物学通报, 2004, 31(5): 136-139.
Fu Guifang, Ma Wanbiao. Chemostat dynamics models described by differential equations(I)［J］. Microbiology China, 2004, 31(5): 136-139.(in Chinese)
［10］ 付桂芳, 马万彪. 由微分方程所描述的微生物连续培养动力系统(II)［J］. 微生物学通报, 2004, 31(6): 128-131.
Fu Guifang, Ma Wanbiao. Chemostat dynamics models described by differential equations(Ⅱ)［J］. Microbiology China, 2004, 31(6): 128-131.(in Chinese)
［11］ 周玉平，周洁. 微生物连续发酵模型及其应用综述［J］. 微生物学通报, 2010, 37(2): 269-273.
Zhou Yuping, Zhou Jie. A review on models of microorganism continuous rermentation and its application［J］. Microbiology China, 2010, 37(2): 269-273.(in Chinese)
［12］ 陆征一, 周义仓. 数学生物学进展［M］. 北京: 科学出版社, 2006.
Lu Zhengyi, Zhou Yicang. Advances in mathematical biology［M］. Beijing：Science Press, 2006.(in Chinese)
［13］ 王洪礼, 高卫楼, 袁其朋. CSTR中生化反应振荡行为研究［J］. 化学反应工程与工艺, 1997, 13(3): 270-275.
Wang Hongli, Gao Weilou, Yuan Qipeng. Study on oscillation behavior of biochemical reaction in CSTR［J］. Chemical Reaction Engineering and Technology, 1997, 13(3): 270-275.(in Chinese)
［14］ 王璐, 原三领, 张同华. 具有Holing II 型功能性作用函数的随机恒化器模型的渐近性态［J］. 高校应用数学学报A 辑, 2012, 27(4): 379-389.
Wang Lu, Yuan Sanling, Zhang Tonghua. Asymptotic properties of a stochastic chemostat model with Holling II functional response［J］. Applied Mathematics: A Journal of Chinese Universities (Series A), 2012, 27(4): 379-389.(in Chinese)
［15］ Mao Xuerong. Stochastic different equations and application［M］. Chichester, UK: Horwood Publishing, 1997.
［16］ Higham D J. An algorithmic introduction to numerical simulation of stochastic differential equations［J］. Siam Review, 2001, 43(3): 525-546.