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Robustness of asymptotic stability to small time delays
1.  Department of Mathematics and Information Science, Yantai University, Yantai 264005 
2.  FB Mathematik, Johann Wolfgang Goethe Universität, Postfach 11 19 32, D60054 Frankfurt a.M. 
[1] 
Volodymyr Pichkur. On practical stability of differential inclusions using Lyapunov functions. Discrete & Continuous Dynamical Systems  B, 2017, 22 (5) : 19771986. doi: 10.3934/dcdsb.2017116 
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Min Zhu, Panpan Ren, Junping Li. Exponential stability of solutions for retarded stochastic differential equations without dissipativity. Discrete & Continuous Dynamical Systems  B, 2017, 22 (7) : 29232938. doi: 10.3934/dcdsb.2017157 
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Tomás Caraballo, Francisco Morillas, José Valero. On differential equations with delay in Banach spaces and attractors for retarded lattice dynamical systems. Discrete & Continuous Dynamical Systems  A, 2014, 34 (1) : 5177. doi: 10.3934/dcds.2014.34.51 
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Anatoli F. Ivanov, Musa A. Mammadov. Global asymptotic stability in a class of nonlinear differential delay equations. Conference Publications, 2011, 2011 (Special) : 727736. doi: 10.3934/proc.2011.2011.727 
[5] 
Michael Schönlein. Asymptotic stability and smooth Lyapunov functions for a class of abstract dynamical systems. Discrete & Continuous Dynamical Systems  A, 2017, 37 (7) : 40534069. doi: 10.3934/dcds.2017172 
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Yejuan Wang, Lin Yang. Global exponential attraction for multivalued semidynamical systems with application to delay differential equations without uniqueness. Discrete & Continuous Dynamical Systems  B, 2019, 24 (4) : 19611987. doi: 10.3934/dcdsb.2018257 
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Tomás Caraballo, José Real, T. Taniguchi. The exponential stability of neutral stochastic delay partial differential equations. Discrete & Continuous Dynamical Systems  A, 2007, 18 (2&3) : 295313. doi: 10.3934/dcds.2007.18.295 
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Ismael Maroto, Carmen Núñez, Rafael Obaya. Exponential stability for nonautonomous functional differential equations with statedependent delay. Discrete & Continuous Dynamical Systems  B, 2017, 22 (8) : 31673197. doi: 10.3934/dcdsb.2017169 
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Evelyn Buckwar, Girolama Notarangelo. A note on the analysis of asymptotic meansquare stability properties for systems of linear stochastic delay differential equations. Discrete & Continuous Dynamical Systems  B, 2013, 18 (6) : 15211531. doi: 10.3934/dcdsb.2013.18.1521 
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Michael Dellnitz, Mirko HesselVon Molo, Adrian Ziessler. On the computation of attractors for delay differential equations. Journal of Computational Dynamics, 2016, 3 (1) : 93112. doi: 10.3934/jcd.2016005 
[11] 
Pham Huu Anh Ngoc. Stability of nonlinear differential systems with delay. Evolution Equations & Control Theory, 2015, 4 (4) : 493505. doi: 10.3934/eect.2015.4.493 
[12] 
Jacson Simsen, José Valero. Global attractors for $p$Laplacian differential inclusions in unbounded domains. Discrete & Continuous Dynamical Systems  B, 2016, 21 (9) : 32393267. doi: 10.3934/dcdsb.2016096 
[13] 
Hammamia Mohamed Ali, Lassaad Mchiria, Sana Netchaoui, Stefanie Sonner. Pullback exponential attractors for differential equations with variable delays. Discrete & Continuous Dynamical Systems  B, 2017, 22 (11) : 119. doi: 10.3934/dcdsb.2019183 
[14] 
Francisco Balibrea, José Valero. On dimension of attractors of differential inclusions and reactiondiffussion equations. Discrete & Continuous Dynamical Systems  A, 1999, 5 (3) : 515528. doi: 10.3934/dcds.1999.5.515 
[15] 
Yulan Lu, Minghui Song, Mingzhu Liu. Convergence rate and stability of the splitstep theta method for stochastic differential equations with piecewise continuous arguments. Discrete & Continuous Dynamical Systems  B, 2019, 24 (2) : 695717. doi: 10.3934/dcdsb.2018203 
[16] 
Junya Nishiguchi. On parameter dependence of exponential stability of equilibrium solutions in differential equations with a single constant delay. Discrete & Continuous Dynamical Systems  A, 2016, 36 (10) : 56575679. doi: 10.3934/dcds.2016048 
[17] 
Loïs Boullu, Mostafa Adimy, Fabien Crauste, Laurent PujoMenjouet. Oscillations and asymptotic convergence for a delay differential equation modeling platelet production. Discrete & Continuous Dynamical Systems  B, 2019, 24 (6) : 24172442. doi: 10.3934/dcdsb.2018259 
[18] 
Frédéric Mazenc, Christophe Prieur. Strict Lyapunov functions for semilinear parabolic partial differential equations. Mathematical Control & Related Fields, 2011, 1 (2) : 231250. doi: 10.3934/mcrf.2011.1.231 
[19] 
Dimitri Breda, Sara Della Schiava. Pseudospectral reduction to compute Lyapunov exponents of delay differential equations. Discrete & Continuous Dynamical Systems  B, 2018, 23 (7) : 27272741. doi: 10.3934/dcdsb.2018092 
[20] 
Leonid Berezansky, Elena Braverman. Stability of linear differential equations with a distributed delay. Communications on Pure & Applied Analysis, 2011, 10 (5) : 13611375. doi: 10.3934/cpaa.2011.10.1361 
2018 Impact Factor: 1.143
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