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Optimal control on hybrid ODE Systems with application to a tick disease model
1.  Department of Mathematics, University of Tennessee, 1403 Circle Drive, Knoxville, TN 379961300, United States 
[1] 
Ping Lin, Weihan Wang. Optimal control problems for some ordinary differential equations with behavior of blowup or quenching. Mathematical Control & Related Fields, 2018, 8 (3&4) : 809828. doi: 10.3934/mcrf.2018036 
[2] 
Lukáš Adam, Jiří Outrata. On optimal control of a sweeping process coupled with an ordinary differential equation. Discrete & Continuous Dynamical Systems  B, 2014, 19 (9) : 27092738. doi: 10.3934/dcdsb.2014.19.2709 
[3] 
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 
[4] 
Zhenyu Lu, Junhao Hu, Xuerong Mao. Stabilisation by delay feedback control for highly nonlinear hybrid stochastic differential equations. Discrete & Continuous Dynamical Systems  B, 2019, 24 (8) : 40994116. doi: 10.3934/dcdsb.2019052 
[5] 
Sébastien Court, Karl Kunisch, Laurent Pfeiffer. Hybrid optimal control problems for a class of semilinear parabolic equations. Discrete & Continuous Dynamical Systems  S, 2018, 11 (6) : 10311060. doi: 10.3934/dcdss.2018060 
[6] 
JanHendrik Webert, Philip E. Gill, SvenJoachim Kimmerle, Matthias Gerdts. A study of structureexploiting SQP algorithms for an optimal control problem with coupled hyperbolic and ordinary differential equation constraints. Discrete & Continuous Dynamical Systems  S, 2018, 11 (6) : 12591282. doi: 10.3934/dcdss.2018071 
[7] 
Yuriy Golovaty, Anna MarciniakCzochra, Mariya Ptashnyk. Stability of nonconstant stationary solutions in a reactiondiffusion equation coupled to the system of ordinary differential equations. Communications on Pure & Applied Analysis, 2012, 11 (1) : 229241. doi: 10.3934/cpaa.2012.11.229 
[8] 
Bernard Dacorogna, Alessandro Ferriero. Regularity and selecting principles for implicit ordinary differential equations. Discrete & Continuous Dynamical Systems  B, 2009, 11 (1) : 87101. doi: 10.3934/dcdsb.2009.11.87 
[9] 
Zvi Artstein. Averaging of ordinary differential equations with slowly varying averages. Discrete & Continuous Dynamical Systems  B, 2010, 14 (2) : 353365. doi: 10.3934/dcdsb.2010.14.353 
[10] 
Tomasz Kapela, Piotr Zgliczyński. A Lohnertype algorithm for control systems and ordinary differential inclusions. Discrete & Continuous Dynamical Systems  B, 2009, 11 (2) : 365385. doi: 10.3934/dcdsb.2009.11.365 
[11] 
Holly Gaff. Preliminary analysis of an agentbased model for a tickborne disease. Mathematical Biosciences & Engineering, 2011, 8 (2) : 463473. doi: 10.3934/mbe.2011.8.463 
[12] 
Shangbing Ai. Global stability of equilibria in a tickborne disease model. Mathematical Biosciences & Engineering, 2007, 4 (4) : 567572. doi: 10.3934/mbe.2007.4.567 
[13] 
Yuyun Zhao, Yi Zhang, Tao Xu, Ling Bai, Qian Zhang. pth moment exponential stability of hybrid stochastic functional differential equations by feedback control based on discretetime state observations. Discrete & Continuous Dynamical Systems  B, 2017, 22 (1) : 209226. doi: 10.3934/dcdsb.2017011 
[14] 
W. Sarlet, G. E. Prince, M. Crampin. Generalized submersiveness of secondorder ordinary differential equations. Journal of Geometric Mechanics, 2009, 1 (2) : 209221. doi: 10.3934/jgm.2009.1.209 
[15] 
Stefano Maset. Conditioning and relative error propagation in linear autonomous ordinary differential equations. Discrete & Continuous Dynamical Systems  B, 2018, 23 (7) : 28792909. doi: 10.3934/dcdsb.2018165 
[16] 
Aeeman Fatima, F. M. Mahomed, Chaudry Masood Khalique. Conditional symmetries of nonlinear thirdorder ordinary differential equations. Discrete & Continuous Dynamical Systems  S, 2018, 11 (4) : 655666. doi: 10.3934/dcdss.2018040 
[17] 
Jean Mawhin, James R. Ward Jr. Guidinglike functions for periodic or bounded solutions of ordinary differential equations. Discrete & Continuous Dynamical Systems  A, 2002, 8 (1) : 3954. doi: 10.3934/dcds.2002.8.39 
[18] 
Alex Bihlo, James Jackaman, Francis Valiquette. On the development of symmetrypreserving finite element schemes for ordinary differential equations. Journal of Computational Dynamics, 2020, 7 (2) : 339368. doi: 10.3934/jcd.2020014 
[19] 
Iasson Karafyllis, Lars Grüne. Feedback stabilization methods for the numerical solution of ordinary differential equations. Discrete & Continuous Dynamical Systems  B, 2011, 16 (1) : 283317. doi: 10.3934/dcdsb.2011.16.283 
[20] 
Alessandro Fonda, Fabio Zanolin. Bounded solutions of nonlinear second order ordinary differential equations. Discrete & Continuous Dynamical Systems  A, 1998, 4 (1) : 9198. doi: 10.3934/dcds.1998.4.91 
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