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Attractors for differential equations with multiple variable delays
1. | Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080 Sevilla |
2. | Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom |
References:
[1] |
T. Caraballo, G. Lukaszewicz and J. Real, Pullback attractors for asymptotically compact non-autonomous dynamical systems,, Nonlinear Anal., 64 (2006), 484.
|
[2] |
T. Caraballo, P. Marín-Rubio and J. Valero, Autonomous and non-autonomous attractors for differential equations with delays,, J. Differential Equations, 208 (2005), 9.
|
[3] |
Tomás Caraballo, José A. Langa and James C. Robinson, Attractors for differential equations with variable delays,, J. Math. Anal. Appl., 260 (2001), 421.
|
[4] |
Huabin Chen, Impulsive-integral inequality and exponential stability for stochastic partial differential equations with delays,, Statist. Probab. Lett., 80 (2010), 50.
|
[5] |
Hans Crauel and Franco Flandoli, Attractors for random dynamical systems,, Probab. Theory Related Fields, 100 (1994), 365.
|
[6] |
Jack K. Hale, "Asymptotic Behavior of Dissipative Systems,", Mathematical Surveys and Monographs, 25 (1988).
|
[7] |
Jack K. Hale and Sjoerd M. Verduyn Lunel, "Introduction to Functional-Differential Equations,", volume 99 of Applied Mathematical Sciences. Springer-Verlag, (1993).
|
[8] |
Gábor Kiss and Bernd Krauskopf, Stability implications of delay distribution for first-order and second-order systems,, Discrete Contin. Dyn. Syst. Ser. B, 13 (2010), 327.
|
[9] |
Gábor Kiss and Bernd Krauskopf, Stabilizing effect of delay distribution for a class of second-order systems without instantaneous feedback,, Dynamical Systems: An International Journal, 26 (2011), 85.
|
[10] |
Gábor Kiss and Jean-Philippe Lessard, Computational fixed point theory for differential delay equations with multiple time lags,, J. Differential Equations, 252 (2012), 3093.
|
[11] |
P. E. Kloeden, Pullback attractors of nonautonomous semidynamical systems,, Stoch. Dyn., 3 (2003), 101.
|
[12] |
Tibor Krisztin, Global dynamics of delay differential equations,, Periodica Mathematica Hungarica, 56 (2008), 83.
|
[13] |
Tibor Krisztin, Hans-Otto Walther and Jianhong Wu, "Shape, Smoothness and Invariant Stratification of an Attracting Set for Delayed Monotone Positive Feedback,", volume 11 of Fields Institute Monographs. American Mathematical Society, (1999).
|
[14] |
Michal Křížek, Numerical experience with the finite speed of gravitational interaction,, Math. Comput. Simulation, 50 (1999), 237.
|
[15] |
Yang Kuang, "Delay Differential Equations with Applications in Population Dynamics,", volume 191 of Mathematics in Science and Engineering. Academic Press Inc., (1993).
|
[16] |
Pedro Marín-Rubio and José Real, On the relation between two different concepts of pullback attractors for non-autonomous dynamical systems,, Nonlinear Anal., 71 (2009), 3956.
|
[17] |
Roger D. Nussbaum, Differential-delay equations with two time lags,, Mem. Amer. Math. Soc., 16 (1978).
|
[18] |
Roger D. Nussbaum, Functional differential equations,, in, 2 (2002), 461.
|
[19] |
Martin Rasmussen, "Attractivity and Bifurcation for Nonautonomous Dynamical Systems,", volume 1907 of Lecture Notes in Mathematics. Springer, (1907).
|
[20] |
B. Schmalfuss, Backward cocycles and attractors of stochastic differential equations,, in, (1992), 185. Google Scholar |
[21] |
George R. Sell, Nonautonomous differential equations and topological dynamics. I. The basic theory,, Trans. Amer. Math. Soc., 127 (1967), 241.
|
[22] |
George R. Sell, Nonautonomous differential equations and topological dynamics. II. Limiting equations,, Trans. Amer. Math. Soc., 127 (1967), 263.
|
[23] |
H. O. Walther, Dynamics of delay differential equations,, in, 205 (2006), 411.
|
show all references
References:
[1] |
T. Caraballo, G. Lukaszewicz and J. Real, Pullback attractors for asymptotically compact non-autonomous dynamical systems,, Nonlinear Anal., 64 (2006), 484.
|
[2] |
T. Caraballo, P. Marín-Rubio and J. Valero, Autonomous and non-autonomous attractors for differential equations with delays,, J. Differential Equations, 208 (2005), 9.
|
[3] |
Tomás Caraballo, José A. Langa and James C. Robinson, Attractors for differential equations with variable delays,, J. Math. Anal. Appl., 260 (2001), 421.
|
[4] |
Huabin Chen, Impulsive-integral inequality and exponential stability for stochastic partial differential equations with delays,, Statist. Probab. Lett., 80 (2010), 50.
|
[5] |
Hans Crauel and Franco Flandoli, Attractors for random dynamical systems,, Probab. Theory Related Fields, 100 (1994), 365.
|
[6] |
Jack K. Hale, "Asymptotic Behavior of Dissipative Systems,", Mathematical Surveys and Monographs, 25 (1988).
|
[7] |
Jack K. Hale and Sjoerd M. Verduyn Lunel, "Introduction to Functional-Differential Equations,", volume 99 of Applied Mathematical Sciences. Springer-Verlag, (1993).
|
[8] |
Gábor Kiss and Bernd Krauskopf, Stability implications of delay distribution for first-order and second-order systems,, Discrete Contin. Dyn. Syst. Ser. B, 13 (2010), 327.
|
[9] |
Gábor Kiss and Bernd Krauskopf, Stabilizing effect of delay distribution for a class of second-order systems without instantaneous feedback,, Dynamical Systems: An International Journal, 26 (2011), 85.
|
[10] |
Gábor Kiss and Jean-Philippe Lessard, Computational fixed point theory for differential delay equations with multiple time lags,, J. Differential Equations, 252 (2012), 3093.
|
[11] |
P. E. Kloeden, Pullback attractors of nonautonomous semidynamical systems,, Stoch. Dyn., 3 (2003), 101.
|
[12] |
Tibor Krisztin, Global dynamics of delay differential equations,, Periodica Mathematica Hungarica, 56 (2008), 83.
|
[13] |
Tibor Krisztin, Hans-Otto Walther and Jianhong Wu, "Shape, Smoothness and Invariant Stratification of an Attracting Set for Delayed Monotone Positive Feedback,", volume 11 of Fields Institute Monographs. American Mathematical Society, (1999).
|
[14] |
Michal Křížek, Numerical experience with the finite speed of gravitational interaction,, Math. Comput. Simulation, 50 (1999), 237.
|
[15] |
Yang Kuang, "Delay Differential Equations with Applications in Population Dynamics,", volume 191 of Mathematics in Science and Engineering. Academic Press Inc., (1993).
|
[16] |
Pedro Marín-Rubio and José Real, On the relation between two different concepts of pullback attractors for non-autonomous dynamical systems,, Nonlinear Anal., 71 (2009), 3956.
|
[17] |
Roger D. Nussbaum, Differential-delay equations with two time lags,, Mem. Amer. Math. Soc., 16 (1978).
|
[18] |
Roger D. Nussbaum, Functional differential equations,, in, 2 (2002), 461.
|
[19] |
Martin Rasmussen, "Attractivity and Bifurcation for Nonautonomous Dynamical Systems,", volume 1907 of Lecture Notes in Mathematics. Springer, (1907).
|
[20] |
B. Schmalfuss, Backward cocycles and attractors of stochastic differential equations,, in, (1992), 185. Google Scholar |
[21] |
George R. Sell, Nonautonomous differential equations and topological dynamics. I. The basic theory,, Trans. Amer. Math. Soc., 127 (1967), 241.
|
[22] |
George R. Sell, Nonautonomous differential equations and topological dynamics. II. Limiting equations,, Trans. Amer. Math. Soc., 127 (1967), 263.
|
[23] |
H. O. Walther, Dynamics of delay differential equations,, in, 205 (2006), 411.
|
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