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On Lyapunov exponents of difference equations with random delay
1. | Institute of Mathematics, Vietnamese Academy of Science and Technology, 18 Hoang Quoc Viet Road, 10307 Hanoi, Vietnam |
2. | Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, 10307 Ha Noi, Vietnam |
3. | Institute for Analysis & Center for Dynamics, Department of Mathematics, Technische Universität Dresden, Zellescher Weg 12-14, 01069 Dresden, Germany |
References:
[1] |
L. Arnold, Random Dynamical Systems,, Springer-Verlag, (1998).
doi: 10.1007/978-3-662-12878-7. |
[2] |
L. Arnold and N. D. Cong, Generic properties of Lyapunov exponents,, Random Comput. Dynam., 2 (1994), 335.
|
[3] |
I. P. Cornfeld, S. V. Fomin and Y. G. Sinaĭ, Ergodic Theory,, Springer-Verlag, (1982).
doi: 10.1007/978-1-4615-6927-5. |
[4] |
H. Crauel, T. S. Doan and S. Siegmund, Difference equations with random delay,, J. Difference Equ. Appl., 15 (2009), 627.
doi: 10.1080/10236190802612865. |
[5] |
T. S. Doan and S. Siegmund, Differential equations with random delay,, Fields Inst. Commun., 64 (2013), 279.
doi: 10.1007/978-1-4614-4523-4_11. |
[6] |
R. C. Ferreira, M. R. S. Briones and F. Antoneli, A model of gene expression based on random dynamical systems reveals modularity properties of gene regulatory networks,, preprint, (2013). Google Scholar |
[7] |
M. J. Garrido-Atienza, A. Ogrowsky and B. Schmalfuss, Random differential equations with random delays,, Stoch. Dyn., 11 (2011), 369.
doi: 10.1142/S0219493711003358. |
[8] |
Y. Hino, S. Murakami and T. Naito, Functional Differential Equations with Infinite Delay,, Lecture Notes in Mathematics, (1473).
|
[9] |
Z. Lian and K. Lu, Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space,, Mem. Amer. Math. Soc., 206 (2010).
doi: 10.1090/S0065-9266-10-00574-0. |
[10] |
P. Walter, An Introduction to Ergodic Theory,, Graduate Texts in Mathematics, (1982).
|
[11] |
F. Wu, G. G. Yin and L. Y. Wang, Stability of a pure random delay system with two-time-scale Markovian switching,, J. Differential Equations, 253 (2012), 878.
doi: 10.1016/j.jde.2012.04.017. |
[12] |
F. Wu and P. E. Kloeden, Mean-square random attractors of stochastic delay differential equations with random delay,, Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 1715.
doi: 10.3934/dcdsb.2013.18.1715. |
show all references
References:
[1] |
L. Arnold, Random Dynamical Systems,, Springer-Verlag, (1998).
doi: 10.1007/978-3-662-12878-7. |
[2] |
L. Arnold and N. D. Cong, Generic properties of Lyapunov exponents,, Random Comput. Dynam., 2 (1994), 335.
|
[3] |
I. P. Cornfeld, S. V. Fomin and Y. G. Sinaĭ, Ergodic Theory,, Springer-Verlag, (1982).
doi: 10.1007/978-1-4615-6927-5. |
[4] |
H. Crauel, T. S. Doan and S. Siegmund, Difference equations with random delay,, J. Difference Equ. Appl., 15 (2009), 627.
doi: 10.1080/10236190802612865. |
[5] |
T. S. Doan and S. Siegmund, Differential equations with random delay,, Fields Inst. Commun., 64 (2013), 279.
doi: 10.1007/978-1-4614-4523-4_11. |
[6] |
R. C. Ferreira, M. R. S. Briones and F. Antoneli, A model of gene expression based on random dynamical systems reveals modularity properties of gene regulatory networks,, preprint, (2013). Google Scholar |
[7] |
M. J. Garrido-Atienza, A. Ogrowsky and B. Schmalfuss, Random differential equations with random delays,, Stoch. Dyn., 11 (2011), 369.
doi: 10.1142/S0219493711003358. |
[8] |
Y. Hino, S. Murakami and T. Naito, Functional Differential Equations with Infinite Delay,, Lecture Notes in Mathematics, (1473).
|
[9] |
Z. Lian and K. Lu, Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space,, Mem. Amer. Math. Soc., 206 (2010).
doi: 10.1090/S0065-9266-10-00574-0. |
[10] |
P. Walter, An Introduction to Ergodic Theory,, Graduate Texts in Mathematics, (1982).
|
[11] |
F. Wu, G. G. Yin and L. Y. Wang, Stability of a pure random delay system with two-time-scale Markovian switching,, J. Differential Equations, 253 (2012), 878.
doi: 10.1016/j.jde.2012.04.017. |
[12] |
F. Wu and P. E. Kloeden, Mean-square random attractors of stochastic delay differential equations with random delay,, Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 1715.
doi: 10.3934/dcdsb.2013.18.1715. |
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