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A priori bounds and periodic solutions for a class of planar systems with applications to LotkaVolterra equations
Feedback control of noise in a 2D nonlinear structural acoustics model
1.  Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 276958212, United States 
2.  ICASE, NASA Langley Research Center, Hampton, VA 23681, United States 
[1] 
Andrew D. Lewis, David R. Tyner. Geometric Jacobian linearization and LQR theory. Journal of Geometric Mechanics, 2010, 2 (4) : 397440. doi: 10.3934/jgm.2010.2.397 
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Sanling Yuan, Yongli Song, Junhui Li. Oscillations in a plasmid turbidostat model with delayed feedback control. Discrete & Continuous Dynamical Systems  B, 2011, 15 (3) : 893914. doi: 10.3934/dcdsb.2011.15.893 
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Shu Zhang, Jian Xu. Timevarying delayed feedback control for an internet congestion control model. Discrete & Continuous Dynamical Systems  B, 2011, 16 (2) : 653668. doi: 10.3934/dcdsb.2011.16.653 
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Guirong Jiang, Qishao Lu. The dynamics of a PreyPredator model with impulsive state feedback control. Discrete & Continuous Dynamical Systems  B, 2006, 6 (6) : 13011320. doi: 10.3934/dcdsb.2006.6.1301 
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Haiying Jing, Zhaoyu Yang. The impact of state feedback control on a predatorprey model with functional response. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 607614. doi: 10.3934/dcdsb.2004.4.607 
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Junyoung Jang, Kihoon Jang, HeeDae Kwon, Jeehyun Lee. Feedback control of an HBV model based on ensemble kalman filter and differential evolution. Mathematical Biosciences & Engineering, 2018, 15 (3) : 667691. doi: 10.3934/mbe.2018030 
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Yuan Tan, Qingyuan Cao, Lan Li, Tianshi Hu, Min Su. A chanceconstrained stochastic model predictive control problem with disturbance feedback. Journal of Industrial & Management Optimization, 2021, 17 (1) : 6779. doi: 10.3934/jimo.2019099 
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Kazuyuki Yagasaki. Optimal control of the SIR epidemic model based on dynamical systems theory. Discrete & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021144 
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Pedro M. Jordan. Finiteamplitude acoustics under the classical theory of particleladen flows. Evolution Equations & Control Theory, 2019, 8 (1) : 101116. doi: 10.3934/eect.2019006 
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Qizhen Xiao, Binxiang Dai. Heteroclinic bifurcation for a general predatorprey model with Allee effect and state feedback impulsive control strategy. Mathematical Biosciences & Engineering, 2015, 12 (5) : 10651081. doi: 10.3934/mbe.2015.12.1065 
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Qiying Hu, Chen Xu, Wuyi Yue. A unified model for state feedback of discrete event systems II: Control synthesis problems. Journal of Industrial & Management Optimization, 2008, 4 (4) : 713726. doi: 10.3934/jimo.2008.4.713 
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Heinz Schättler, Urszula Ledzewicz. Perturbation feedback control: A geometric interpretation. Numerical Algebra, Control & Optimization, 2012, 2 (3) : 631654. doi: 10.3934/naco.2012.2.631 
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Antonio Fernández, Pedro L. García. Regular discretizations in optimal control theory. Journal of Geometric Mechanics, 2013, 5 (4) : 415432. doi: 10.3934/jgm.2013.5.415 
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K. Renee Fister, Jennifer Hughes Donnelly. Immunotherapy: An Optimal Control Theory Approach. Mathematical Biosciences & Engineering, 2005, 2 (3) : 499510. doi: 10.3934/mbe.2005.2.499 
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Rohit Gupta, Farhad Jafari, Robert J. Kipka, Boris S. Mordukhovich. Linear openness and feedback stabilization of nonlinear control systems. Discrete & Continuous Dynamical Systems  S, 2018, 11 (6) : 11031119. doi: 10.3934/dcdss.2018063 
[16] 
Fatihcan M. Atay. Delayed feedback control near Hopf bifurcation. Discrete & Continuous Dynamical Systems  S, 2008, 1 (2) : 197205. doi: 10.3934/dcdss.2008.1.197 
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Elena Braverman, Alexandra Rodkina. Stabilization of difference equations with noisy proportional feedback control. Discrete & Continuous Dynamical Systems  B, 2017, 22 (6) : 20672088. doi: 10.3934/dcdsb.2017085 
[18] 
Daniel Franco, Chris Guiver, Phoebe Smith, Stuart Townley. A switching feedback control approach for persistence of managed resources. Discrete & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021109 
[19] 
Barbara Kaltenbacher. Mathematics of nonlinear acoustics. Evolution Equations & Control Theory, 2015, 4 (4) : 447491. doi: 10.3934/eect.2015.4.447 
[20] 
K.F.C. Yiu, K.L. Mak, K. L. Teo. Airfoil design via optimal control theory. Journal of Industrial & Management Optimization, 2005, 1 (1) : 133148. doi: 10.3934/jimo.2005.1.133 
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