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Local and global phase portrait of equation $\dot z=f(z)$
On periodic orbits of polynomial relay systems
1. | Institut de Mathématiques de Bourgogne, UMR CNRS 5584, Université de Bourgogne, Dijon, France |
2. | Instituto de Matemática e Estatística, University of Campinas, Campinas, Brazil |
[1] |
Jędrzej Śniatycki. Integral curves of derivations on locally semi-algebraic differential spaces. Conference Publications, 2003, 2003 (Special) : 827-833. doi: 10.3934/proc.2003.2003.827 |
[2] |
Jan Sieber. Finding periodic orbits in state-dependent delay differential equations as roots of algebraic equations. Discrete and Continuous Dynamical Systems, 2012, 32 (8) : 2607-2651. doi: 10.3934/dcds.2012.32.2607 |
[3] |
Yingjie Bi, Siyu Liu, Yong Li. Periodic solutions of differential-algebraic equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (4) : 1383-1395. doi: 10.3934/dcdsb.2019232 |
[4] |
Nicola Guglielmi, Christian Lubich. Numerical periodic orbits of neutral delay differential equations. Discrete and Continuous Dynamical Systems, 2005, 13 (4) : 1057-1067. doi: 10.3934/dcds.2005.13.1057 |
[5] |
Luca Dieci, Timo Eirola, Cinzia Elia. Periodic orbits of planar discontinuous system under discretization. Discrete and Continuous Dynamical Systems - B, 2018, 23 (7) : 2743-2762. doi: 10.3934/dcdsb.2018103 |
[6] |
Joan Gimeno, Àngel Jorba. Using automatic differentiation to compute periodic orbits of delay differential equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (12) : 4853-4867. doi: 10.3934/dcdsb.2020130 |
[7] |
Wan-Tong Li, Bin-Guo Wang. Attractor minimal sets for nonautonomous type-K competitive and semi-convex delay differential equations with applications. Discrete and Continuous Dynamical Systems, 2009, 24 (2) : 589-611. doi: 10.3934/dcds.2009.24.589 |
[8] |
Karsten Matthies. Exponentially small splitting of homoclinic orbits of parabolic differential equations under periodic forcing. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 585-602. doi: 10.3934/dcds.2003.9.585 |
[9] |
Vu Hoang Linh, Volker Mehrmann. Spectral analysis for linear differential-algebraic equations. Conference Publications, 2011, 2011 (Special) : 991-1000. doi: 10.3934/proc.2011.2011.991 |
[10] |
Cristopher Hermosilla. Stratified discontinuous differential equations and sufficient conditions for robustness. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 4415-4437. doi: 10.3934/dcds.2015.35.4415 |
[11] |
Jan Sieber, Matthias Wolfrum, Mark Lichtner, Serhiy Yanchuk. On the stability of periodic orbits in delay equations with large delay. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 3109-3134. doi: 10.3934/dcds.2013.33.3109 |
[12] |
Ábel Garab. Unique periodic orbits of a delay differential equation with piecewise linear feedback function. Discrete and Continuous Dynamical Systems, 2013, 33 (6) : 2369-2387. doi: 10.3934/dcds.2013.33.2369 |
[13] |
Armengol Gasull, Héctor Giacomini, Maite Grau. On the stability of periodic orbits for differential systems in $\mathbb{R}^n$. Discrete and Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 495-509. doi: 10.3934/dcdsb.2008.10.495 |
[14] |
Jason R. Scott, Stephen Campbell. Auxiliary signal design for failure detection in differential-algebraic equations. Numerical Algebra, Control and Optimization, 2014, 4 (2) : 151-179. doi: 10.3934/naco.2014.4.151 |
[15] |
B. Coll, A. Gasull, R. Prohens. Center-focus and isochronous center problems for discontinuous differential equations. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 609-624. doi: 10.3934/dcds.2000.6.609 |
[16] |
Yingxiang Xu, Yongkui Zou. Preservation of homoclinic orbits under discretization of delay differential equations. Discrete and Continuous Dynamical Systems, 2011, 31 (1) : 275-299. doi: 10.3934/dcds.2011.31.275 |
[17] |
M. Sumon Hossain, M. Monir Uddin. Iterative methods for solving large sparse Lyapunov equations and application to model reduction of index 1 differential-algebraic-equations. Numerical Algebra, Control and Optimization, 2019, 9 (2) : 173-186. doi: 10.3934/naco.2019013 |
[18] |
Enrique Zuazua. Controllability of partial differential equations and its semi-discrete approximations. Discrete and Continuous Dynamical Systems, 2002, 8 (2) : 469-513. doi: 10.3934/dcds.2002.8.469 |
[19] |
Miguel Mendes. A note on the coding of orbits in certain discontinuous maps. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 369-382. doi: 10.3934/dcds.2010.27.369 |
[20] |
Tiago de Carvalho, Rodrigo Donizete Euzébio, Jaume Llibre, Durval José Tonon. Detecting periodic orbits in some 3D chaotic quadratic polynomial differential systems. Discrete and Continuous Dynamical Systems - B, 2016, 21 (1) : 1-11. doi: 10.3934/dcdsb.2016.21.1 |
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