Random Dynamical Systems and Random Maps

2013 ◽  
pp. 35-83
Keyword(s):  
Dynamical Systems ◽  
Random Dynamical Systems ◽  
Random Maps

scholarly journals METASTABILITY, LYAPUNOV EXPONENTS, ESCAPE RATES, AND TOPOLOGICAL ENTROPY IN RANDOM DYNAMICAL SYSTEMS

2013 ◽  
Vol 13 (04) ◽  
pp. 1350004 ◽  
Author(s):  
GARY FROYLAND ◽  
OGNJEN STANCEVIC
Keyword(s):  
Dynamical Systems ◽  
Finite Type ◽  
Topological Entropy ◽  
Lower Bounds ◽  
Random Systems ◽  
Random Dynamical Systems ◽  
Upper And Lower Bounds ◽  
Random System ◽  
Random Maps ◽  
Frobenius Operator

We explore the concept of metastability in random dynamical systems, focusing on connections between random Perron–Frobenius operator cocycles and escape rates of random maps, and on topological entropy of random shifts of finite type. The Lyapunov spectrum of the random Perron–Frobenius cocycle and the random adjacency matrix cocycle is used to decompose the random system into two disjoint random systems with rigorous upper and lower bounds on (i) the escape rate in the setting of random maps, and (ii) topological entropy in the setting of random shifts of finite type, respectively.

scholarly journals On the Concept of Complexity of Random Dynamical Systems

1998 ◽  
Vol 12 (03) ◽  
pp. 225-243 ◽  
Author(s):  
V. Loreto ◽  
M. Serva ◽  
A. Vulpiani
Keyword(s):  
Experimental Data ◽  
Dynamical Systems ◽  
Random Perturbation ◽  
Point Of View ◽  
Random Dynamical Systems ◽  
Random Perturbations ◽  
Physical Point ◽  
Random Maps ◽  
Numerical Examples ◽  
Real Experimental Data

We show how to introduce a characterization the "complexity" of random dynamical systems. More precisely we propose a suitable indicator of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by these systems. This indicator of complexity, which can be extracted from real experimental data, turns out to be very natural in the context of information theory. For dynamical systems with random perturbations, it coincides with the rate K of divergence of nearby trajectories evolving under two different noise realizations. In presence of strong dynamical intermittency, the value of K is very different from the standard Lyapunov exponent λσ computed through the consideration of two nearby trajectories evolving under the same realization of the random perturbation. However, the former is much more relevant than the latter from a physical point of view as illustrated by some numerical examples of noisy and random maps.

VARIATIONAL PRINCIPLE FOR SUBADDITIVE SEQUENCE OF POTENTIALS IN BUNDLE RANDOM DYNAMICAL SYSTEMS

2009 ◽  
Vol 09 (02) ◽  
pp. 205-215 ◽  
Author(s):  
XIANFENG MA ◽  
ERCAI CHEN
Keyword(s):  
Dynamical Systems ◽  
Variational Principle ◽  
Multifractal Analysis ◽  
Weak Condition ◽  
Random Dynamical Systems ◽  
Topological Pressure ◽  
Set Up

The topological pressure is defined for subadditive sequence of potentials in bundle random dynamical systems. A variational principle for the topological pressure is set up in a very weak condition. The result may have some applications in the study of multifractal analysis for random version of nonconformal dynamical systems.

Noise-induced unstable dimension variability and transition to chaos in random dynamical systems

2003 ◽  
Vol 67 (2) ◽  
Author(s):  
Ying-Cheng Lai ◽  
Zonghua Liu ◽  
Lora Billings ◽  
Ira B. Schwartz
Keyword(s):  
Dynamical Systems ◽  
Random Dynamical Systems ◽  
Transition To Chaos

scholarly journals A random dynamical systems perspective on stochastic resonance

Nonlinearity ◽  
2017 ◽  
Vol 30 (7) ◽  
pp. 2835-2853 ◽  
Author(s):  
Anna Maria Cherubini ◽  
Jeroen S W Lamb ◽  
Martin Rasmussen ◽  
Yuzuru Sato
Keyword(s):  
Dynamical Systems ◽  
Stochastic Resonance ◽  
Random Dynamical Systems ◽  
Systems Perspective
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