A Behavioral Characterization of Discrete Time Dynamical Systems over Directed Graphs

被引：2

作者：

Ackerman, Jonathan ^{[1
]}

Ayers, Kimberly ^{[1
]}

Beltran, Eduardo J. ^{[2
]}

Bonet, Joshua ^{[2
]}

Lu, Devin ^{[3
]}

Rudelius, Thomas ^{[4
]}

机构：

[1] Bowdoin Coll, Dept Math, Brunswick, ME 04011 USA

[2] Univ Puerto Rico, Dept Math, Rio Piedras, PR 00931 USA

[3] Stanford Univ, Dept Math, Stanford, CA 94309 USA

[4] Cornell Univ, Dept Math, Ithaca, NY 14850 USA

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2014年 / 13卷 / 01期

基金：

美国国家科学基金会;

关键词：

Morse Decomposition; Morse Sets; Shift Space; Symbolic Dynamical System; Recurrent Chain;

D O I：

10.1007/s12346-014-0111-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using a directed graph, a Markov chain can be treated as a dynamical system over a compact space of bi-infinite sequences, with a flow given by the left shift of a sequence. In this paper, we show that the Morse sets of the finest Morse decomposition on this space can be related to communicating classes of the directed graph by considering lifting the communicating classes to the shift space. Finally, we prove that the flow restricted to these Morse sets is chaotic.

引用

页码：161 / 180

页数：20

共 50 条

[41] Control problems of discrete-time dynamical systems
Hasegawa, Yasumichi
Lecture Notes in Control and Information Sciences, 2013, 447
[42] Chain recurrence in multidimensional time discrete dynamical systems
Oprocha, Piotr
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2008, 20 (04) : 1039 - 1056
[43] Flatness and Submersivity of Discrete-Time Dynamical Systems
Guillot, Philippe
Millerioux, Gilles
IEEE CONTROL SYSTEMS LETTERS, 2020, 4 (02): : 337 - 342
[44] Dimensionality reduction in discrete-time dynamical systems
Tu, Chengyi
Wu, Yu
Luo, Jianhong
Jiang, Yi
Pan, Xuwei
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2023, 123
[45] Chaos of time-varying discrete dynamical systems
Shi, Yuming
Chen, Guanrong
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2009, 15 (05) : 429 - 449
[46] Symplectic Property of Discrete-Time Dynamical Systems
Sogo, Kiyoshi
Uno, Toshiaki
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2011, 80 (12)
[47] On Ω-limit sets of discrete-time dynamical systems
Kempf, R
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2002, 8 (12) : 1121 - 1131
[48] Generations of solvable discrete-time dynamical systems
Bihun, Oksana
Calogero, Francesco
JOURNAL OF MATHEMATICAL PHYSICS, 2017, 58 (05)
[49] Forward Attractors in Discrete Time Nonautonomous Dynamical Systems
Kloeden, Peter E.
Lorenz, Thomas
Yang, Meihua
DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH APPLICATIONS, ICDDEA 2015, 2016, 164 : 313 - 322
[50] Computational complexity studies of synchronous Boolean finite dynamical systems on directed graphs
Ogihara, Mitsunori
Uchizawa, Kei
INFORMATION AND COMPUTATION, 2017, 256 : 226 - 236

← 1 2 3 4 5 →