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Journal articles on the topic 'Non-autonomous dynamical systems'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

N. Carvalho, Alexandre, José A. Langa, and James C. Robinson. "Non-autonomous dynamical systems." Discrete & Continuous Dynamical Systems - B 20, no. 3 (2015): 703–47. http://dx.doi.org/10.3934/dcdsb.2015.20.703.

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2

Anzaldo-Meneses, A. "On non-autonomous dynamical systems." Journal of Mathematical Physics 56, no. 4 (April 2015): 042702. http://dx.doi.org/10.1063/1.4916893.

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3

Cavro, Jakub. "Recurrence in non-autonomous dynamical systems." Journal of Difference Equations and Applications 25, no. 9-10 (August 9, 2019): 1404–11. http://dx.doi.org/10.1080/10236198.2019.1651849.

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4

Momeni, Davood, Phongpichit Channuie, and Mudhahir Al Ajmi. "Mapping of non-autonomous dynamical systems to autonomous ones." International Journal of Geometric Methods in Modern Physics 16, no. 06 (June 2019): 1950089. http://dx.doi.org/10.1142/s0219887819500890.

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Using a proper choice of the dynamical variables, we show that a non-autonomous dynamical system transforming to an autonomous dynamical system with a certain coordinate transformations can be obtained by solving a general nonlinear first-order partial differential equations. We examine some special cases and provide particular physical examples. Our framework constitutes general machineries in investigating other non-autonomous dynamical systems.

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5

Cheban, David. "Sell’s conjecture for non-autonomous dynamical systems." Nonlinear Analysis: Theory, Methods & Applications 75, no. 7 (May 2012): 3393–406. http://dx.doi.org/10.1016/j.na.2012.01.002.

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6

Leon, Manuel de, and Paulo R. Rodrigues. "Dynamical connections and non-autonomous lagrangian systems." Annales de la faculté des sciences de Toulouse Mathématiques 9, no. 2 (1988): 171–81. http://dx.doi.org/10.5802/afst.655.

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7

Huang, Qiuling, Yuming Shi, and Lijuan Zhang. "Sensitivity of non-autonomous discrete dynamical systems." Applied Mathematics Letters 39 (January 2015): 31–34. http://dx.doi.org/10.1016/j.aml.2014.08.007.

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8

Schechter, Martin. "Periodic non-autonomous second-order dynamical systems." Journal of Differential Equations 223, no. 2 (April 2006): 290–302. http://dx.doi.org/10.1016/j.jde.2005.02.022.

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9

Shao, Hua, Hao Zhu, and Guanrong Chen. "On fuzzifications of non-autonomous dynamical systems." Topology and its Applications 297 (June 2021): 107704. http://dx.doi.org/10.1016/j.topol.2021.107704.

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10

Chen, Xiaopeng, and Jinqiao Duan. "State space decomposition for non-autonomous dynamical systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 141, no. 5 (September 26, 2011): 957–74. http://dx.doi.org/10.1017/s0308210510000661.

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The decomposition of state spaces into dynamically different components is helpful for understanding dynamics of complex systems. A Conley-type decomposition theorem is proved for non-autonomous dynamical systems defined on a non-compact but separable state space. Specifically, the state space can be decomposed into a chain-recurrent part and a gradient-like part. This result applies to both non-autonomous ordinary differential equations on a Euclidean space (which is only locally compact), and to non-autonomous partial differential equations on an infinite-dimensional function space (which is not even locally compact). This decomposition result is demonstrated by discussing a few concrete examples, such as the Lorenz system and the Navier–Stokes system, under time-dependent forcing.

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11

Ding, Xian-Feng, Tian-Xiu Lu, and Jian-Jun Wang. "Sensitivity of non-autonomous discrete dynamical systems revisited." Journal of Nonlinear Sciences and Applications 10, no. 10 (October 19, 2017): 5239–44. http://dx.doi.org/10.22436/jnsa.010.10.10.

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12

Lan, Yaoyao, and Alfred Peris. "Weak stability of non-autonomous discrete dynamical systems." Topology and its Applications 250 (December 2018): 53–60. http://dx.doi.org/10.1016/j.topol.2018.10.006.

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13

Robinson, James C., and Grzegorz Łukaszewicz. "Invariant measures for non-autonomous dissipative dynamical systems." Discrete and Continuous Dynamical Systems 34, no. 10 (April 2014): 4211–22. http://dx.doi.org/10.3934/dcds.2014.34.4211.

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14

Cheban, David. "Markus–Yamabe conjecture for non-autonomous dynamical systems." Nonlinear Analysis: Theory, Methods & Applications 95 (January 2014): 202–18. http://dx.doi.org/10.1016/j.na.2013.09.010.

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15

Schechter, Martin. "Ground state solutions for non-autonomous dynamical systems." Journal of Mathematical Physics 55, no. 10 (October 2014): 101504. http://dx.doi.org/10.1063/1.4897443.

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16

Blanes, S., and F. Casas. "Splitting methods for non-autonomous separable dynamical systems." Journal of Physics A: Mathematical and General 39, no. 19 (April 24, 2006): 5405–23. http://dx.doi.org/10.1088/0305-4470/39/19/s05.

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17

Kloeden, Peter E., and C. Pötzsche. "Non-autonomous difference equations and discrete dynamical systems." Journal of Difference Equations and Applications 17, no. 2 (February 2011): 129–30. http://dx.doi.org/10.1080/10236198.2010.549001.

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18

Sacker, Robert J. "Geometric theory of discrete non-autonomous dynamical systems." Journal of Difference Equations and Applications 20, no. 3 (December 5, 2013): 506–10. http://dx.doi.org/10.1080/10236198.2013.864469.

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19

Ju, Xuewei, Desheng Li, Chunqiu Li, and Ailing Qi. "Approximate Forward Attractors of Non-Autonomous Dynamical Systems." Chinese Annals of Mathematics, Series B 40, no. 4 (June 14, 2019): 541–54. http://dx.doi.org/10.1007/s11401-019-0150-8.

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20

Cui, Hongyong, and José A. Langa. "Uniform attractors for non-autonomous random dynamical systems." Journal of Differential Equations 263, no. 2 (July 2017): 1225–68. http://dx.doi.org/10.1016/j.jde.2017.03.018.

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21

Navascués, M. A. "New equilibria of non-autonomous discrete dynamical systems." Chaos, Solitons & Fractals 152 (November 2021): 111413. http://dx.doi.org/10.1016/j.chaos.2021.111413.

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22

Mao, An-Min, and Miao-Miao Yang. "Periodic Solutions to Non-Autonomous Second-Order Dynamical Systems." Advances in Pure Mathematics 01, no. 03 (2011): 90–94. http://dx.doi.org/10.4236/apm.2011.13020.

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23

Zgurovsky, Michael, Mark Gluzman, Nataliia Gorban, Pavlo Kasyanov, Liliia Paliichuk, and Olha Khomenko. "Uniform global attractors for non-autonomous dissipative dynamical systems." Discrete & Continuous Dynamical Systems - B 22, no. 5 (2017): 2053–65. http://dx.doi.org/10.3934/dcdsb.2017120.

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24

Caraballo, T., G. Łukaszewicz, and J. Real. "Pullback attractors for asymptotically compact non-autonomous dynamical systems." Nonlinear Analysis: Theory, Methods & Applications 64, no. 3 (February 2006): 484–98. http://dx.doi.org/10.1016/j.na.2005.03.111.

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25

CARVALHO, ALEXANDRE N., JOSÉ A. LANGA, and JAMES C. ROBINSON. "Lower semicontinuity of attractors for non-autonomous dynamical systems." Ergodic Theory and Dynamical Systems 29, no. 6 (February 3, 2009): 1765–80. http://dx.doi.org/10.1017/s0143385708000850.

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AbstractThis paper is concerned with the lower semicontinuity of attractors for semilinear non-autonomous differential equations in Banach spaces. We require the unperturbed attractor to be given as the union of unstable manifolds of time-dependent hyperbolic solutions, generalizing previous results valid only for gradient-like systems in which the hyperbolic solutions are equilibria. The tools employed are a study of the continuity of the local unstable manifolds of the hyperbolic solutions and results on the continuity of the exponential dichotomy of the linearization around each of these solutions.

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26

Rezaali, E., F. H. Ghane, and H. Parham. "Ergodic shadowing of non-autonomous discrete-time dynamical systems." International Journal of Dynamical Systems and Differential Equations 9, no. 2 (2019): 203. http://dx.doi.org/10.1504/ijdsde.2019.10022227.

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27

Parham, H., F. H. Ghane, and E. Rezaali. "Ergodic shadowing of non-autonomous discrete-time dynamical systems." International Journal of Dynamical Systems and Differential Equations 9, no. 2 (2019): 203. http://dx.doi.org/10.1504/ijdsde.2019.100572.

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28

Johnson, Russell, and Víctor Muñoz-Villarragut. "Some questions concerning attractors for non-autonomous dynamical systems." Nonlinear Analysis: Theory, Methods & Applications 71, no. 12 (December 2009): e1858-e1868. http://dx.doi.org/10.1016/j.na.2009.02.088.

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29

Bonotto, Everaldo M., Matheus C. Bortolan, Tomás Caraballo, and Rodolfo Collegari. "Impulsive non-autonomous dynamical systems and impulsive cocycle attractors." Mathematical Methods in the Applied Sciences 40, no. 4 (June 28, 2016): 1095–113. http://dx.doi.org/10.1002/mma.4038.

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30

Góra, Paweł, Abraham Boyarsky, and Christopher Keefe. "Absolutely continuous invariant measures for non-autonomous dynamical systems." Journal of Mathematical Analysis and Applications 470, no. 1 (February 2019): 159–68. http://dx.doi.org/10.1016/j.jmaa.2018.09.060.

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31

Prieto-Martínez, Pedro Daniel, and Narciso Román-Roy. "Unified formalism for higher order non-autonomous dynamical systems." Journal of Mathematical Physics 53, no. 3 (March 2012): 032901. http://dx.doi.org/10.1063/1.3692326.

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32

Cui, Hongyong, and Peter E. Kloeden. "Invariant forward attractors of non-autonomous random dynamical systems." Journal of Differential Equations 265, no. 12 (December 2018): 6166–86. http://dx.doi.org/10.1016/j.jde.2018.07.028.

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33

Vasisht, Radhika, and Ruchi Das. "Induced dynamics in hyperspaces of non-autonomous discrete systems." Filomat 33, no. 7 (2019): 1911–20. http://dx.doi.org/10.2298/fil1907911v.

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In this paper, the interrelations of some dynamical properties of a non-autonomous dynamical system (X, f1, ?) and its induced non-autonomous dynamical system (K(X), f1, ?) are studied, where K(X) is the hyperspace of all non-empty compact subsets of X, endowed with Vietoris topology. Various stronger forms of sensitivity and transitivity are considered. Some examples of non-autonomous systems are provided to support the results. A relation between shadowing property of the non-autonomous system (X, f1, ?) and its induced system (K(X), f1, ?) is studied.

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34

Balibrea, Francisco. "On problems of Topological Dynamics in non-autonomous discrete systems." Applied Mathematics and Nonlinear Sciences 1, no. 2 (September 28, 2016): 391–404. http://dx.doi.org/10.21042/amns.2016.2.00034.

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AbstractMost of problems in Topological Dynamics in the theory of general autonomous discrete dynamical systems have been addressed in the non-autonomous setting. In this paper we will review some of them, giving references and stating open questions.

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35

Efendiev, M., S. Zelik, and A. Miranville. "Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 135, no. 4 (August 2005): 703–30. http://dx.doi.org/10.1017/s030821050000408x.

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We suggest in this paper a new explicit algorithm allowing us to construct exponential attractors which are uniformly Hölder continuous with respect to the variation of the dynamical system in some natural large class. Moreover, we extend this construction to non-autonomous dynamical systems (dynamical processes) treating in that case the exponential attractor as a uniformly exponentially attracting, finite-dimensional and time-dependent set in the phase space. In particular, this result shows that, for a wide class of non-autonomous equations of mathematical physics, the limit dynamics remains finite dimensional no matter how complicated the dependence of the external forces on time is. We illustrate the main results of this paper on the model example of a non-autonomous reaction–diffusion system in a bounded domain.

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36

Liao, Xinyuan, Caidi Zhao, and Shengfan Zhou. "Compact uniform attractors for dissipative non-autonomous lattice dynamical systems." Communications on Pure & Applied Analysis 6, no. 4 (2007): 1087–111. http://dx.doi.org/10.3934/cpaa.2007.6.1087.

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37

Kawan, Christoph, and Yuri Latushkin. "Some results on the entropy of non-autonomous dynamical systems." Dynamical Systems 31, no. 3 (November 26, 2015): 251–79. http://dx.doi.org/10.1080/14689367.2015.1111299.

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38

Krabs, Werner. "Stability and Controllability in Non-autonomous Time-discrete Dynamical Systems." Journal of Difference Equations and Applications 8, no. 12 (January 2002): 1107–18. http://dx.doi.org/10.1080/1023619021000053971.

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39

Shao, Hua, Guanrong Chen, and Yuming Shi. "Some criteria of chaos in non-autonomous discrete dynamical systems." Journal of Difference Equations and Applications 26, no. 3 (February 7, 2020): 295–308. http://dx.doi.org/10.1080/10236198.2020.1725496.

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40

Bonotto, E. M., M. C. Bortolan, T. Caraballo, and R. Collegari. "Attractors for impulsive non-autonomous dynamical systems and their relations." Journal of Differential Equations 262, no. 6 (March 2017): 3524–50. http://dx.doi.org/10.1016/j.jde.2016.11.036.

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41

Chu, Jifeng, Pedro J. Torres, and Meirong Zhang. "Periodic solutions of second order non-autonomous singular dynamical systems." Journal of Differential Equations 239, no. 1 (August 2007): 196–212. http://dx.doi.org/10.1016/j.jde.2007.05.007.

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42

You, Bo. "Pullback exponential attractors for some non‐autonomous dissipative dynamical systems." Mathematical Methods in the Applied Sciences 44, no. 13 (April 30, 2021): 10361–86. http://dx.doi.org/10.1002/mma.7413.

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43

Imran, Mohamedsh, and Ihsan Jabbar Kadhim. "Non-autonomous invariant sets and attractors: Random dynamical system." Al-Qadisiyah Journal Of Pure Science 25, no. 4 (August 25, 2020): 17–23. http://dx.doi.org/10.29350/qjps.2020.25.4.1166.

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In this paper the concepts of pullback attractor ,pullback absorbing family in (deterministic) dynamical system are defined in (random) dynamical systems. Also some main result such as (existence) of pullback attractors ,upper semi-continuous of pullback attractors and uniform and global attractors are proved in random dynamical system .

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44

Astrelina, A. A. "The Baire Class of Topological Entropy of Non–Autonomous Dynamical Systems." Moscow University Mathematics Bulletin 73, no. 5 (September 2018): 203–6. http://dx.doi.org/10.3103/s0027132218050078.

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45

Mayer, Volker, Bartlomiej Skorulski, and Mariusz Urbanski. "Regularity and irregularity of fiber dimensions of non-autonomous dynamical systems." Annales Academiae Scientiarum Fennicae Mathematica 38 (June 2013): 489–514. http://dx.doi.org/10.5186/aasfm.2013.3829.

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46

Dellnitz, Michael, and Christian Horenkamp. "The efficient approximation of coherent pairs in non-autonomous dynamical systems." Discrete & Continuous Dynamical Systems - A 32, no. 9 (2012): 3029–42. http://dx.doi.org/10.3934/dcds.2012.32.3029.

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47

Wang, Bixiang. "Multivalued non-autonomous random dynamical systems for wave equations without uniqueness." Discrete & Continuous Dynamical Systems - B 22, no. 5 (2017): 2011–51. http://dx.doi.org/10.3934/dcdsb.2017119.

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48

Abdallah, Ahmed Y. "Uniform exponential attractors for first order non-autonomous lattice dynamical systems." Journal of Differential Equations 251, no. 6 (September 2011): 1489–504. http://dx.doi.org/10.1016/j.jde.2011.05.030.

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49

Shao, Hua, Yuming Shi, and Hao Zhu. "Relationships among some chaotic properties of non-autonomous discrete dynamical systems." Journal of Difference Equations and Applications 24, no. 7 (April 3, 2018): 1055–64. http://dx.doi.org/10.1080/10236198.2018.1458101.

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50

Abdallah, Ahmed Y. "Uniform global attractors for first order non-autonomous lattice dynamical systems." Proceedings of the American Mathematical Society 138, no. 09 (September 1, 2010): 3219. http://dx.doi.org/10.1090/s0002-9939-10-10440-7.

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