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A mathematical and numerical study of incompressible flows with a surfactant monolayer
Asynchronous time integration for polynomial chaos expansion of uncertain periodic dynamics
1.  LIMSICNRS, UPR 3251, BP 133, Orsay F91403, France, France 
2.  Johns Hopkins University, Department of Mechanical Engineering, Baltimore, MD 21218, United States 
3.  Florida State University, Computational Science & Engineering – Department of Mathematics, Tallahassee, FL 323064510, United States 
[1] 
Valery A. Gaiko. The geometry of limit cycle bifurcations in polynomial dynamical systems. Conference Publications, 2011, 2011 (Special) : 447456. doi: 10.3934/proc.2011.2011.447 
[2] 
José Miguel Pasini, Tuhin Sahai. Polynomial chaos based uncertainty quantification in Hamiltonian, multitime scale, and chaotic systems. Journal of Computational Dynamics, 2014, 1 (2) : 357375. doi: 10.3934/jcd.2014.1.357 
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Andrew J. Majda, Michal Branicki. Lessons in uncertainty quantification for turbulent dynamical systems. Discrete & Continuous Dynamical Systems  A, 2012, 32 (9) : 31333221. doi: 10.3934/dcds.2012.32.3133 
[4] 
Jaume Llibre, Claudia Valls. Algebraic limit cycles for quadratic polynomial differential systems. Discrete & Continuous Dynamical Systems  B, 2018, 23 (6) : 24752485. doi: 10.3934/dcdsb.2018070 
[5] 
Jihua Yang, Liqin Zhao. Limit cycle bifurcations for piecewise smooth integrable differential systems. Discrete & Continuous Dynamical Systems  B, 2017, 22 (6) : 24172425. doi: 10.3934/dcdsb.2017123 
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Elena Goncharova, Maxim Staritsyn. Optimal control of dynamical systems with polynomial impulses. Discrete & Continuous Dynamical Systems  A, 2015, 35 (9) : 43674384. doi: 10.3934/dcds.2015.35.4367 
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Marta Štefánková. Inheriting of chaos in uniformly convergent nonautonomous dynamical systems on the interval. Discrete & Continuous Dynamical Systems  A, 2016, 36 (6) : 34353443. doi: 10.3934/dcds.2016.36.3435 
[8] 
Hongyong Cui, Peter E. Kloeden, Meihua Yang. Forward omega limit sets of nonautonomous dynamical systems. Discrete & Continuous Dynamical Systems  S, 2020, 13 (4) : 11031114. doi: 10.3934/dcdss.2020065 
[9] 
Freddy Dumortier. Sharp upperbounds for the number of large amplitude limit cycles in polynomial Lienard systems. Discrete & Continuous Dynamical Systems  A, 2012, 32 (5) : 14651479. doi: 10.3934/dcds.2012.32.1465 
[10] 
Armengol Gasull, Hector Giacomini. Upper bounds for the number of limit cycles of some planar polynomial differential systems. Discrete & Continuous Dynamical Systems  A, 2010, 27 (1) : 217229. doi: 10.3934/dcds.2010.27.217 
[11] 
Helmut Rüssmann. KAM iteration with nearly infinitely small steps in dynamical systems of polynomial character. Discrete & Continuous Dynamical Systems  S, 2010, 3 (4) : 683718. doi: 10.3934/dcdss.2010.3.683 
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Vadim S. Anishchenko, Tatjana E. Vadivasova, Galina I. Strelkova, George A. Okrokvertskhov. Statistical properties of dynamical chaos. Mathematical Biosciences & Engineering, 2004, 1 (1) : 161184. doi: 10.3934/mbe.2004.1.161 
[13] 
Lijun Wei, Xiang Zhang. Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems. Discrete & Continuous Dynamical Systems  A, 2016, 36 (5) : 28032825. doi: 10.3934/dcds.2016.36.2803 
[14] 
Elena K. Kostousova. On polyhedral estimates for trajectory tubes of dynamical discretetime systems with multiplicative uncertainty. Conference Publications, 2011, 2011 (Special) : 864873. doi: 10.3934/proc.2011.2011.864 
[15] 
Jakub Šotola. Relationship between LiYorke chaos and positive topological sequence entropy in nonautonomous dynamical systems. Discrete & Continuous Dynamical Systems  A, 2018, 38 (10) : 51195128. doi: 10.3934/dcds.2018225 
[16] 
Luca Dieci, Cinzia Elia, Dingheng Pi. Limit cycles for regularized discontinuous dynamical systems with a hyperplane of discontinuity. Discrete & Continuous Dynamical Systems  B, 2017, 22 (8) : 30913112. doi: 10.3934/dcdsb.2017165 
[17] 
Oliver DíazEspinosa, Rafael de la Llave. Renormalization and central limit theorem for critical dynamical systems with weak external noise. Journal of Modern Dynamics, 2007, 1 (3) : 477543. doi: 10.3934/jmd.2007.1.477 
[18] 
Ben Niu, Weihua Jiang. Dynamics of a limit cycle oscillator with extended delay feedback. Discrete & Continuous Dynamical Systems  B, 2013, 18 (5) : 14391458. doi: 10.3934/dcdsb.2013.18.1439 
[19] 
Jianhe Shen, Maoan Han. Bifurcations of canard limit cycles in several singularly perturbed generalized polynomial Liénard systems. Discrete & Continuous Dynamical Systems  A, 2013, 33 (7) : 30853108. doi: 10.3934/dcds.2013.33.3085 
[20] 
Flaviano Battelli, Michal Fe?kan. Chaos in forced impact systems. Discrete & Continuous Dynamical Systems  S, 2013, 6 (4) : 861890. doi: 10.3934/dcdss.2013.6.861 
2018 Impact Factor: 1.143
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