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Integrators for highly oscillatory Hamiltonian systems: An homogenization approach
Stability implications of delay distribution for firstorder and secondorder systems
1.  Department of Engineering Mathematics, University of Bristol, Bristol BS8 1TR, United Kingdom 
2.  Bristol Center for Applied Nonlinear Mathematics, Department of Engineering Mathematics, University of Bristol, Queen's Building, Bristol BS8 1TR 
[1] 
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 
[2] 
Tian Zhang, Huabin Chen, Chenggui Yuan, Tomás Caraballo. On the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equations. Discrete & Continuous Dynamical Systems  B, 2017, 22 (11) : 121. doi: 10.3934/dcdsb.2019062 
[3] 
Zhenyu Lu, Junhao Hu, Xuerong Mao. Stabilisation by delay feedback control for highly nonlinear hybrid stochastic differential equations. Discrete & Continuous Dynamical Systems  B, 2019, 24 (8) : 40994116. doi: 10.3934/dcdsb.2019052 
[4] 
Samuel Bernard, Fabien Crauste. Optimal linear stability condition for scalar differential equations with distributed delay. Discrete & Continuous Dynamical Systems  B, 2015, 20 (7) : 18551876. doi: 10.3934/dcdsb.2015.20.1855 
[5] 
Samuel Bernard, Jacques Bélair, Michael C Mackey. Sufficient conditions for stability of linear differential equations with distributed delay. Discrete & Continuous Dynamical Systems  B, 2001, 1 (2) : 233256. doi: 10.3934/dcdsb.2001.1.233 
[6] 
Jehad O. Alzabut. A necessary and sufficient condition for the existence of periodic solutions of linear impulsive differential equations with distributed delay. Conference Publications, 2007, 2007 (Special) : 3543. doi: 10.3934/proc.2007.2007.35 
[7] 
Elena Braverman, Sergey Zhukovskiy. Absolute and delaydependent stability of equations with a distributed delay. Discrete & Continuous Dynamical Systems  A, 2012, 32 (6) : 20412061. doi: 10.3934/dcds.2012.32.2041 
[8] 
Tomás Caraballo, Renato Colucci, Luca Guerrini. Bifurcation scenarios in an ordinary differential equation with constant and distributed delay: A case study. Discrete & Continuous Dynamical Systems  B, 2019, 24 (6) : 26392655. doi: 10.3934/dcdsb.2018268 
[9] 
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 
[10] 
Hermann Brunner, Stefano Maset. Time transformations for delay differential equations. Discrete & Continuous Dynamical Systems  A, 2009, 25 (3) : 751775. doi: 10.3934/dcds.2009.25.751 
[11] 
Klaudiusz Wójcik, Piotr Zgliczyński. Topological horseshoes and delay differential equations. Discrete & Continuous Dynamical Systems  A, 2005, 12 (5) : 827852. doi: 10.3934/dcds.2005.12.827 
[12] 
Serhiy Yanchuk, Leonhard Lücken, Matthias Wolfrum, Alexander Mielke. Spectrum and amplitude equations for scalar delaydifferential equations with large delay. Discrete & Continuous Dynamical Systems  A, 2015, 35 (1) : 537553. doi: 10.3934/dcds.2015.35.537 
[13] 
Nicola Guglielmi, Christian Lubich. Numerical periodic orbits of neutral delay differential equations. Discrete & Continuous Dynamical Systems  A, 2005, 13 (4) : 10571067. doi: 10.3934/dcds.2005.13.1057 
[14] 
Eduardo Liz, Gergely Röst. On the global attractor of delay differential equations with unimodal feedback. Discrete & Continuous Dynamical Systems  A, 2009, 24 (4) : 12151224. doi: 10.3934/dcds.2009.24.1215 
[15] 
Alfonso RuizHerrera. Chaos in delay differential equations with applications in population dynamics. Discrete & Continuous Dynamical Systems  A, 2013, 33 (4) : 16331644. doi: 10.3934/dcds.2013.33.1633 
[16] 
Eduardo Liz, Manuel Pinto, Gonzalo Robledo, Sergei Trofimchuk, Victor Tkachenko. Wright type delay differential equations with negative Schwarzian. Discrete & Continuous Dynamical Systems  A, 2003, 9 (2) : 309321. doi: 10.3934/dcds.2003.9.309 
[17] 
C. M. Groothedde, J. D. Mireles James. Parameterization method for unstable manifolds of delay differential equations. Journal of Computational Dynamics, 2017, 4 (1&2) : 2170. doi: 10.3934/jcd.2017002 
[18] 
Igor Chueshov, Michael Scheutzow. Invariance and monotonicity for stochastic delay differential equations. Discrete & Continuous Dynamical Systems  B, 2013, 18 (6) : 15331554. doi: 10.3934/dcdsb.2013.18.1533 
[19] 
Jan Čermák, Jana Hrabalová. Delaydependent stability criteria for neutral delay differential and difference equations. Discrete & Continuous Dynamical Systems  A, 2014, 34 (11) : 45774588. doi: 10.3934/dcds.2014.34.4577 
[20] 
Aissa Guesmia, Nassereddine Tatar. Some wellposedness and stability results for abstract hyperbolic equations with infinite memory and distributed time delay. Communications on Pure & Applied Analysis, 2015, 14 (2) : 457491. doi: 10.3934/cpaa.2015.14.457 
2018 Impact Factor: 1.008
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