# American Institute of Mathematical Sciences

2001, 2001(Special): 229-240. doi: 10.3934/proc.2001.2001.229

## The unstable set of zero and the global attractor for delayed monotone positive feedback

 1 Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged

Published  November 2013

Citation: Tibor Krisztin. The unstable set of zero and the global attractor for delayed monotone positive feedback. Conference Publications, 2001, 2001 (Special) : 229-240. doi: 10.3934/proc.2001.2001.229
 [1] Eduardo Liz, Gergely Röst. On the global attractor of delay differential equations with unimodal feedback. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1215-1224. doi: 10.3934/dcds.2009.24.1215 [2] Arne Ogrowsky, Björn Schmalfuss. Unstable invariant manifolds for a nonautonomous differential equation with nonautonomous unbounded delay. Discrete and Continuous Dynamical Systems - B, 2013, 18 (6) : 1663-1681. doi: 10.3934/dcdsb.2013.18.1663 [3] C. M. Groothedde, J. D. Mireles James. Parameterization method for unstable manifolds of delay differential equations. Journal of Computational Dynamics, 2017, 4 (1&2) : 21-70. doi: 10.3934/jcd.2017002 [4] Xiuli Sun, Rong Yuan, Yunfei Lv. Global Hopf bifurcations of neutral functional differential equations with state-dependent delay. Discrete and Continuous Dynamical Systems - B, 2018, 23 (2) : 667-700. doi: 10.3934/dcdsb.2018038 [5] Tibor Krisztin. A local unstable manifold for differential equations with state-dependent delay. Discrete and Continuous Dynamical Systems, 2003, 9 (4) : 993-1028. doi: 10.3934/dcds.2003.9.993 [6] Zhihua Liu, Pierre Magal. Functional differential equation with infinite delay in a space of exponentially bounded and uniformly continuous functions. Discrete and Continuous Dynamical Systems - B, 2020, 25 (6) : 2271-2292. doi: 10.3934/dcdsb.2019227 [7] Bao-Zhu Guo, Li-Ming Cai. A note for the global stability of a delay differential equation of hepatitis B virus infection. Mathematical Biosciences & Engineering, 2011, 8 (3) : 689-694. doi: 10.3934/mbe.2011.8.689 [8] Yirong Jiang, Nanjing Huang, Zhouchao Wei. Existence of a global attractor for fractional differential hemivariational inequalities. Discrete and Continuous Dynamical Systems - B, 2020, 25 (4) : 1193-1212. doi: 10.3934/dcdsb.2019216 [9] Dimitri Breda, Sara Della Schiava. Pseudospectral reduction to compute Lyapunov exponents of delay differential equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (7) : 2727-2741. doi: 10.3934/dcdsb.2018092 [10] Ovide Arino, Eva Sánchez. A saddle point theorem for functional state-dependent delay differential equations. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 687-722. doi: 10.3934/dcds.2005.12.687 [11] Ismael Maroto, Carmen NÚÑez, Rafael Obaya. Dynamical properties of nonautonomous functional differential equations with state-dependent delay. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 3939-3961. doi: 10.3934/dcds.2017167 [12] Ismael Maroto, Carmen Núñez, Rafael Obaya. Exponential stability for nonautonomous functional differential equations with state-dependent delay. Discrete and Continuous Dynamical Systems - B, 2017, 22 (8) : 3167-3197. doi: 10.3934/dcdsb.2017169 [13] Jianhua Huang, Yanbin Tang, Ming Wang. Singular support of the global attractor for a damped BBM equation. Discrete and Continuous Dynamical Systems - B, 2021, 26 (10) : 5321-5335. doi: 10.3934/dcdsb.2020345 [14] Biyue Chen, Chunxiang Zhao, Chengkui Zhong. The global attractor for the wave equation with nonlocal strong damping. Discrete and Continuous Dynamical Systems - B, 2021, 26 (12) : 6207-6228. doi: 10.3934/dcdsb.2021015 [15] Wenjun Liu, Hefeng Zhuang. Global attractor for a suspension bridge problem with a nonlinear delay term in the internal feedback. Discrete and Continuous Dynamical Systems - B, 2021, 26 (2) : 907-942. doi: 10.3934/dcdsb.2020147 [16] Changjing Zhuge, Xiaojuan Sun, Jinzhi Lei. On positive solutions and the Omega limit set for a class of delay differential equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (9) : 2487-2503. doi: 10.3934/dcdsb.2013.18.2487 [17] Benjamin B. Kennedy. A state-dependent delay equation with negative feedback and "mildly unstable" rapidly oscillating periodic solutions. Discrete and Continuous Dynamical Systems - B, 2013, 18 (6) : 1633-1650. doi: 10.3934/dcdsb.2013.18.1633 [18] Eric Benoît. Bifurcation delay - the case of the sequence: Stable focus - unstable focus - unstable node. Discrete and Continuous Dynamical Systems - S, 2009, 2 (4) : 911-929. doi: 10.3934/dcdss.2009.2.911 [19] Chunhong Li, Jiaowan Luo. Stochastic invariance for neutral functional differential equation with non-lipschitz coefficients. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3299-3318. doi: 10.3934/dcdsb.2018321 [20] Defei Zhang, Ping He. Functional solution about stochastic differential equation driven by $G$-Brownian motion. Discrete and Continuous Dynamical Systems - B, 2015, 20 (1) : 281-293. doi: 10.3934/dcdsb.2015.20.281

Impact Factor: