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Analysis of a model of nutrient driven selfcycling fermentation allowing unimodal response functions
1.  Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada, Canada 
[1] 
Guangjun Shen, Xueying Wu, Xiuwei Yin. Stabilization of stochastic differential equations driven by GLévy process with discretetime feedback control. Discrete & Continuous Dynamical Systems  B, 2021, 26 (2) : 755774. doi: 10.3934/dcdsb.2020133 
[2] 
Yunfei Peng, X. Xiang. A class of nonlinear impulsive differential equation and optimal controls on time scales. Discrete & Continuous Dynamical Systems  B, 2011, 16 (4) : 11371155. doi: 10.3934/dcdsb.2011.16.1137 
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Jiaohui Xu, Tomás Caraballo. Long time behavior of fractional impulsive stochastic differential equations with infinite delay. Discrete & Continuous Dynamical Systems  B, 2019, 24 (6) : 27192743. doi: 10.3934/dcdsb.2018272 
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Xiaohong Li, Mingxin Sun, Zhaohua Gong, Enmin Feng. Multistage optimal control for microbial fedbatch fermentation process. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021040 
[5] 
Hongwei Lou, Weihan Wang. Optimal blowup/quenching time for controlled autonomous ordinary differential equations. Mathematical Control & Related Fields, 2015, 5 (3) : 517527. doi: 10.3934/mcrf.2015.5.517 
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Zengyun Wang, Jinde Cao, Zuowei Cai, Lihong Huang. Finitetime stability of impulsive differential inclusion: Applications to discontinuous impulsive neural networks. Discrete & Continuous Dynamical Systems  B, 2021, 26 (5) : 26772692. doi: 10.3934/dcdsb.2020200 
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Yong Ren, Xuejuan Jia, Lanying Hu. Exponential stability of solutions to impulsive stochastic differential equations driven by $G$Brownian motion. Discrete & Continuous Dynamical Systems  B, 2015, 20 (7) : 21572169. doi: 10.3934/dcdsb.2015.20.2157 
[8] 
Tomás Caraballo, Carlos Ogouyandjou, Fulbert Kuessi Allognissode, Mamadou Abdoul Diop. Existence and exponential stability for neutral stochastic integro–differential equations with impulses driven by a Rosenblatt process. Discrete & Continuous Dynamical Systems  B, 2020, 25 (2) : 507528. doi: 10.3934/dcdsb.2019251 
[9] 
Shaokuan Chen, Shanjian Tang. Semilinear backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process. Mathematical Control & Related Fields, 2015, 5 (3) : 401434. doi: 10.3934/mcrf.2015.5.401 
[10] 
Hermann Brunner, Stefano Maset. Time transformations for delay differential equations. Discrete & Continuous Dynamical Systems, 2009, 25 (3) : 751775. doi: 10.3934/dcds.2009.25.751 
[11] 
Hui Meng, Fei Lung Yuen, Tak Kuen Siu, Hailiang Yang. Optimal portfolio in a continuoustime selfexciting threshold model. Journal of Industrial & Management Optimization, 2013, 9 (2) : 487504. doi: 10.3934/jimo.2013.9.487 
[12] 
Ishak Alia. Timeinconsistent stochastic optimal control problems: a backward stochastic partial differential equations approach. Mathematical Control & Related Fields, 2020, 10 (4) : 785826. doi: 10.3934/mcrf.2020020 
[13] 
Y. Peng, X. Xiang. Second order nonlinear impulsive timevariant systems with unbounded perturbation and optimal controls. Journal of Industrial & Management Optimization, 2008, 4 (1) : 1732. doi: 10.3934/jimo.2008.4.17 
[14] 
Brahim El Asri, Sehail Mazid. Stochastic impulse control Problem with state and time dependent cost functions. Mathematical Control & Related Fields, 2020, 10 (4) : 855875. doi: 10.3934/mcrf.2020022 
[15] 
X. Xiang, Y. Peng, W. Wei. A general class of nonlinear impulsive integral differential equations and optimal controls on Banach spaces. Conference Publications, 2005, 2005 (Special) : 911919. doi: 10.3934/proc.2005.2005.911 
[16] 
Yuefen Chen, Yuanguo Zhu. Indefinite LQ optimal control with process state inequality constraints for discretetime uncertain systems. Journal of Industrial & Management Optimization, 2018, 14 (3) : 913930. doi: 10.3934/jimo.2017082 
[17] 
Kim Dang Phung, Gengsheng Wang, Xu Zhang. On the existence of time optimal controls for linear evolution equations. Discrete & Continuous Dynamical Systems  B, 2007, 8 (4) : 925941. doi: 10.3934/dcdsb.2007.8.925 
[18] 
Ahuod Alsheri, Ebraheem O. Alzahrani, Asim Asiri, Mohamed M. ElDessoky, Yang Kuang. Tumor growth dynamics with nutrient limitation and cell proliferation time delay. Discrete & Continuous Dynamical Systems  B, 2017, 22 (10) : 37713782. doi: 10.3934/dcdsb.2017189 
[19] 
Monica Motta. Minimum time problem with impulsive and ordinary controls. Discrete & Continuous Dynamical Systems, 2018, 38 (11) : 57815809. doi: 10.3934/dcds.2018252 
[20] 
Deepak Kumar, Ahmad Jazlan, Victor Sreeram, Roberto Togneri. Partial fraction expansion based frequency weighted model reduction for discretetime systems. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 329337. doi: 10.3934/naco.2016015 
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