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On some properties and limit cycles of Lienard systems
Linearized stability in functional differential equations with state-dependent delays
| 1. | Department of Mathematics and Computing, University of Veszprém, H-8201 Veszprém, P.O.Box 158, Hungary |
| 2. | Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75083 |
| [1] |
Ismael Maroto, Carmen Núñez, Rafael Obaya. Exponential stability for nonautonomous functional differential equations with state-dependent delay. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3167-3197. doi: 10.3934/dcdsb.2017169 |
| [2] |
Redouane Qesmi, Hans-Otto Walther. Center-stable manifolds for differential equations with state-dependent delays. Discrete & Continuous Dynamical Systems - A, 2009, 23 (3) : 1009-1033. doi: 10.3934/dcds.2009.23.1009 |
| [3] |
Ferenc Hartung. Parameter estimation by quasilinearization in differential equations with state-dependent delays. Discrete & Continuous Dynamical Systems - B, 2013, 18 (6) : 1611-1631. doi: 10.3934/dcdsb.2013.18.1611 |
| [4] |
Ovide Arino, Eva Sánchez. A saddle point theorem for functional state-dependent delay differential equations. Discrete & Continuous Dynamical Systems - A, 2005, 12 (4) : 687-722. doi: 10.3934/dcds.2005.12.687 |
| [5] |
Ismael Maroto, Carmen NÚÑez, Rafael Obaya. Dynamical properties of nonautonomous functional differential equations with state-dependent delay. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3939-3961. doi: 10.3934/dcds.2017167 |
| [6] |
Eugen Stumpf. Local stability analysis of differential equations with state-dependent delay. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 3445-3461. doi: 10.3934/dcds.2016.36.3445 |
| [7] |
Xiuli Sun, Rong Yuan, Yunfei Lv. Global Hopf bifurcations of neutral functional differential equations with state-dependent delay. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 667-700. doi: 10.3934/dcdsb.2018038 |
| [8] |
A. R. Humphries, O. A. DeMasi, F. M. G. Magpantay, F. Upham. Dynamics of a delay differential equation with multiple state-dependent delays. Discrete & Continuous Dynamical Systems - A, 2012, 32 (8) : 2701-2727. doi: 10.3934/dcds.2012.32.2701 |
| [9] |
Tibor Krisztin. A local unstable manifold for differential equations with state-dependent delay. Discrete & Continuous Dynamical Systems - A, 2003, 9 (4) : 993-1028. doi: 10.3934/dcds.2003.9.993 |
| [10] |
Hermann Brunner, Stefano Maset. Time transformations for state-dependent delay differential equations. Communications on Pure & Applied Analysis, 2010, 9 (1) : 23-45. doi: 10.3934/cpaa.2010.9.23 |
| [11] |
Cónall Kelly, Alexandra Rodkina. Constrained stability and instability of polynomial difference equations with state-dependent noise. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 913-933. doi: 10.3934/dcdsb.2009.11.913 |
| [12] |
István Györi, Ferenc Hartung. Exponential stability of a state-dependent delay system. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 773-791. doi: 10.3934/dcds.2007.18.773 |
| [13] |
Jan Sieber. Finding periodic orbits in state-dependent delay differential equations as roots of algebraic equations. Discrete & Continuous Dynamical Systems - A, 2012, 32 (8) : 2607-2651. doi: 10.3934/dcds.2012.32.2607 |
| [14] |
F. M. G. Magpantay, A. R. Humphries. Generalised Lyapunov-Razumikhin techniques for scalar state-dependent delay differential equations. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 85-104. doi: 10.3934/dcdss.2020005 |
| [15] |
Hermann Brunner, Chunhua Ou. On the asymptotic stability of Volterra functional equations with vanishing delays. Communications on Pure & Applied Analysis, 2015, 14 (2) : 397-406. doi: 10.3934/cpaa.2015.14.397 |
| [16] |
Benjamin B. Kennedy. Multiple periodic solutions of state-dependent threshold delay equations. Discrete & Continuous Dynamical Systems - A, 2012, 32 (5) : 1801-1833. doi: 10.3934/dcds.2012.32.1801 |
| [17] |
Odo Diekmann, Karolína Korvasová. Linearization of solution operators for state-dependent delay equations: A simple example. Discrete & Continuous Dynamical Systems - A, 2016, 36 (1) : 137-149. doi: 10.3934/dcds.2016.36.137 |
| [18] |
Shangzhi Li, Shangjiang Guo. Dynamics of a two-species stage-structured model incorporating state-dependent maturation delays. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1393-1423. doi: 10.3934/dcdsb.2017067 |
| [19] |
Alexander V. Rezounenko, Petr Zagalak. Non-local PDEs with discrete state-dependent delays: Well-posedness in a metric space. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 819-835. doi: 10.3934/dcds.2013.33.819 |
| [20] |
Joseph M. Mahaffy, Timothy C. Busken. Regions of stability for a linear differential equation with two rationally dependent delays. Discrete & Continuous Dynamical Systems - A, 2015, 35 (10) : 4955-4986. doi: 10.3934/dcds.2015.35.4955 |
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