scholarly journals Principal Lyapunov Exponents and Principal Floquet Spaces of Positive Random Dynamical Systems. III. Parabolic Equations and Delay Systems

2015 ◽  
Vol 28 (3-4) ◽  
pp. 1039-1079 ◽  
Author(s):  
Janusz Mierczyński ◽  
Wenxian Shen
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Parabolic Equations ◽  
Random Dynamical Systems ◽  
Delay Systems

Random entropy expansiveness for diffeomorphisms with dominated splittings

2019 ◽  
Vol 20 (02) ◽  
pp. 2050014
Author(s):  
Zeya Mi
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Random Dynamical Systems ◽  
Local Entropy ◽  
Dominated Splitting ◽  
One Dimensional ◽  
Hyperbolic Diffeomorphisms ◽  
Partially Hyperbolic ◽  
Bowen Balls ◽  
Partially Hyperbolic Diffeomorphisms

We study the local entropy of typical infinite Bowen balls in random dynamical systems, and show the random entropy expansiveness for [Formula: see text] partially hyperbolic diffeomorphisms with multi one-dimensional centers. Moreover, we consider [Formula: see text] diffeomorphism [Formula: see text] with dominated splitting [Formula: see text] such that [Formula: see text] for every [Formula: see text], and all the Lyapunov exponents are non-negative along [Formula: see text] and non-positive along [Formula: see text], we prove the asymptotically random entropy expansiveness for [Formula: see text].

Transmission of Signals via Synchronization of Chaotic Time-Delay Systems

1998 ◽  
Vol 08 (09) ◽  
pp. 1839-1842 ◽  
Author(s):  
K. Pyragas
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Secure Communication ◽  
Chaotic Synchronization ◽  
Strange Attractors ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Complex Time ◽  
Time Signals

Secure communication via chaotic synchronization is demonstrated using dynamical systems governed by delay deferential equations. Strange attractors of such systems can have an arbitrarily large number of positive Lyapunov exponents giving rise to very complex time signals. This features can provide high security of masked messages.

Pullback attractors for multi-valued non-compact random dynamical systems generated by semi-linear degenerate parabolic equations with unbounded delays

2016 ◽  
Vol 16 (05) ◽  
pp. 1750001 ◽  
Author(s):  
Jingyu Wang ◽  
Yejuan Wang ◽  
Dun Zhao
Keyword(s):  
Dynamical Systems ◽  
Parabolic Equations ◽  
Random Dynamical Systems ◽  
Degenerate Parabolic Equations ◽  
Pullback Attractors ◽  
Asymptotic Compactness ◽  
Unbounded Delay ◽  
Bounded Set ◽  
Degenerate Parabolic ◽  
Linear Degenerate

The theory of pullback attractors for multi-valued non-compact random dynamical systems and a method of asymptotic compactness based on the concepts of the Kuratowski measure of the non-compactness of a bounded set are used to prove the existence of pullback attractors for the multi-valued non-compact random dynamical systems associated with the semi-linear degenerate parabolic unbounded delay equations with both deterministic and random external terms.

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