
Previous Article
Existence of strictly decreasing positive solutions of linear differential equations of neutral type
 DCDSS Home
 This Issue

Next Article
Longtime behavior of positive solutions of a differential equation with statedependent delay
A periodic solution with nonsimple oscillation for an equation with statedependent delay and strictly monotonic negative feedback
Department of Mathematics, Gettysburg College, 300 N. Washington St., Gettysburg, PA 17325, USA 
$ \begin{equation*} x'(t) = f(x(t  d(x_t))), \end{equation*} $ 
$ q $ 
$ q_t \mapsto (q(t),q(t  d(q_t))) $ 
$ q $ 
References:
[1] 
B. B. Kennedy, The PoincaréBendixson theorem for a class of delay equations with statedependent delay and monotonic feedback, preprint. 
[2] 
T. Krisztin and O. Arino, The twodimensional attractor of a differential equation with statedependent delay, Journal of Dynamics and Differential Equations, 13 (2001), 453522. doi: 10.1023/A:1016635223074. 
[3] 
J. MalletParet and R. D. Nussbaum, Boundary layer phenomena for differentialdelay equations with statedependent time lags, I, Arch. Rational Mech. Anal., 120 (1992), 99146. doi: 10.1007/BF00418497. 
[4] 
J. MalletParet and G. R. Sell, Systems of differential delay equations: The PoincaréBendixson theorem for monotone cyclic feedback systems with delay, Journal of Differential Equations, 125 (1996), 441489. doi: 10.1006/jdeq.1996.0037. 
[5] 
H.O. Walther, Algebraicdelay differential systems, statedependent delay, and temporal order of reactions, Journal of Dynamics and Differential Equations, 21 (2009), 195232. doi: 10.1007/s1088400991296. 
[6] 
H.O. Walther, A homoclinic loop generated by variable delay, Journal of Dynamics and Differential Equations, 27 (2015), 11011139. doi: 10.1007/s1088401393332. 
show all references
References:
[1] 
B. B. Kennedy, The PoincaréBendixson theorem for a class of delay equations with statedependent delay and monotonic feedback, preprint. 
[2] 
T. Krisztin and O. Arino, The twodimensional attractor of a differential equation with statedependent delay, Journal of Dynamics and Differential Equations, 13 (2001), 453522. doi: 10.1023/A:1016635223074. 
[3] 
J. MalletParet and R. D. Nussbaum, Boundary layer phenomena for differentialdelay equations with statedependent time lags, I, Arch. Rational Mech. Anal., 120 (1992), 99146. doi: 10.1007/BF00418497. 
[4] 
J. MalletParet and G. R. Sell, Systems of differential delay equations: The PoincaréBendixson theorem for monotone cyclic feedback systems with delay, Journal of Differential Equations, 125 (1996), 441489. doi: 10.1006/jdeq.1996.0037. 
[5] 
H.O. Walther, Algebraicdelay differential systems, statedependent delay, and temporal order of reactions, Journal of Dynamics and Differential Equations, 21 (2009), 195232. doi: 10.1007/s1088400991296. 
[6] 
H.O. Walther, A homoclinic loop generated by variable delay, Journal of Dynamics and Differential Equations, 27 (2015), 11011139. doi: 10.1007/s1088401393332. 
[1] 
Ovide Arino, Eva Sánchez. A saddle point theorem for functional statedependent delay differential equations. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 687722. doi: 10.3934/dcds.2005.12.687 
[2] 
William Clark, Anthony Bloch, Leonardo Colombo. A PoincaréBendixson theorem for hybrid systems. Mathematical Control and Related Fields, 2020, 10 (1) : 2745. doi: 10.3934/mcrf.2019028 
[3] 
Odo Diekmann, Karolína Korvasová. Linearization of solution operators for statedependent delay equations: A simple example. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 137149. doi: 10.3934/dcds.2016.36.137 
[4] 
Benjamin B. Kennedy. Multiple periodic solutions of statedependent threshold delay equations. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 18011833. doi: 10.3934/dcds.2012.32.1801 
[5] 
HansOtto Walther. On Poisson's statedependent delay. Discrete and Continuous Dynamical Systems, 2013, 33 (1) : 365379. doi: 10.3934/dcds.2013.33.365 
[6] 
István Györi, Ferenc Hartung. Exponential stability of a statedependent delay system. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 773791. doi: 10.3934/dcds.2007.18.773 
[7] 
Benjamin B. Kennedy. A statedependent delay equation with negative feedback and "mildly unstable" rapidly oscillating periodic solutions. Discrete and Continuous Dynamical Systems  B, 2013, 18 (6) : 16331650. doi: 10.3934/dcdsb.2013.18.1633 
[8] 
Jan Sieber. Finding periodic orbits in statedependent delay differential equations as roots of algebraic equations. Discrete and Continuous Dynamical Systems, 2012, 32 (8) : 26072651. doi: 10.3934/dcds.2012.32.2607 
[9] 
Xiang Li, Zhixiang Li. Kernel sections and (almost) periodic solutions of a nonautonomous parabolic PDE with a discrete statedependent delay. Communications on Pure and Applied Analysis, 2011, 10 (2) : 687700. doi: 10.3934/cpaa.2011.10.687 
[10] 
D. P. Demuner, M. Federson, C. Gutierrez. The PoincaréBendixson Theorem on the Klein bottle for continuous vector fields. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 495509. doi: 10.3934/dcds.2009.25.495 
[11] 
HansOtto Walther. On solution manifolds of differential systems with discrete statedependent delays. Discrete and Continuous Dynamical Systems  S, 2022 doi: 10.3934/dcdss.2022108 
[12] 
Qingwen Hu. A model of regulatory dynamics with thresholdtype statedependent delay. Mathematical Biosciences & Engineering, 2018, 15 (4) : 863882. doi: 10.3934/mbe.2018039 
[13] 
Shangzhi Li, Shangjiang Guo. Dynamics of a stagestructured population model with a statedependent delay. Discrete and Continuous Dynamical Systems  B, 2020, 25 (9) : 35233551. doi: 10.3934/dcdsb.2020071 
[14] 
Tibor Krisztin. A local unstable manifold for differential equations with statedependent delay. Discrete and Continuous Dynamical Systems, 2003, 9 (4) : 9931028. doi: 10.3934/dcds.2003.9.993 
[15] 
Qingwen Hu, Bernhard LaniWayda, Eugen Stumpf. Preface: Delay differential equations with statedependent delays and their applications. Discrete and Continuous Dynamical Systems  S, 2020, 13 (1) : ii. doi: 10.3934/dcdss.20201i 
[16] 
Eugen Stumpf. Local stability analysis of differential equations with statedependent delay. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 34453461. doi: 10.3934/dcds.2016.36.3445 
[17] 
Ismael Maroto, Carmen NÚÑez, Rafael Obaya. Dynamical properties of nonautonomous functional differential equations with statedependent delay. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 39393961. doi: 10.3934/dcds.2017167 
[18] 
A. R. Humphries, O. A. DeMasi, F. M. G. Magpantay, F. Upham. Dynamics of a delay differential equation with multiple statedependent delays. Discrete and Continuous Dynamical Systems, 2012, 32 (8) : 27012727. doi: 10.3934/dcds.2012.32.2701 
[19] 
Hermann Brunner, Stefano Maset. Time transformations for statedependent delay differential equations. Communications on Pure and Applied Analysis, 2010, 9 (1) : 2345. doi: 10.3934/cpaa.2010.9.23 
[20] 
Matthias Büger, Marcus R.W. Martin. Stabilizing control for an unbounded statedependent delay equation. Conference Publications, 2001, 2001 (Special) : 5665. doi: 10.3934/proc.2001.2001.56 
2021 Impact Factor: 1.865
Tools
Metrics
Other articles
by authors
[Back to Top]