Phase transitions in thermodynamics of a local lyapunov exponent for fully-developed chaotic systems

1992 ◽  
Vol 66 (3-4) ◽  
pp. 727-754 ◽  
Author(s):  
H. Shigematsu
Keyword(s):  
Phase Transitions ◽  
Lyapunov Exponent ◽  
Chaotic Systems ◽  
Local Lyapunov Exponent

MUTUAL AND SELF-COMPOUNDING OF CHAOTIC SYSTEMS

1996 ◽  
Vol 06 (04) ◽  
pp. 759-767
Author(s):  
R. SINGH ◽  
P.S. MOHARIR ◽  
V.M. MARU
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Dynamic Systems ◽  
Mantle Convection ◽  
Chaotic Systems ◽  
Compound System ◽  
Two Systems

The notion of compounding a chaotic system was introduced earlier. It consisted of varying the parameters of the compoundee system in proportion to the variables of the compounder system, resulting in a compound system which has in general higher Lyapunov exponents. Here, the notion is extended to self-compounding of a system with a real-earth example, and mutual compounding of dynamic systems. In the former, the variables in a system perturb its parameters. In the latter, two systems affect the parameters of each other in proportion to their variables. Examples of systems in such compounding relationships are studied. The existence of self-compounding is indicated in the geodynamics of mantle convection. The effect of mutual compounding is studied in terms of Lyapunov exponent variations.

scholarly journals SUPREME LOCAL LYAPUNOV EXPONENTS AND CHAOTIC IMPULSIVE SYNCHRONIZATION

2013 ◽  
Vol 23 (10) ◽  
pp. 1350169 ◽  
Author(s):  
SHENGYAO CHEN ◽  
FENG XI ◽  
ZHONG LIU
Keyword(s):  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Finite Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
Local Instability ◽  
Impulsive Synchronization ◽  
Local Lyapunov Exponent ◽  
Expansion Behavior

Impulsively synchronized chaos with criterion from conditional Lyapunov exponent is often interrupted by desynchronized bursts. This is because the Lyapunov exponent cannot characterize local instability of synchronized attractor. To predict the possibility of the local instability, we introduce a concept of supreme local Lyapunov exponent (SLLE), which is defined as supremum of local Lyapunov exponents over the attractor. The SLLE is independent of the system trajectories and therefore, can characterize the extreme expansion behavior in all local regions with prescribed finite-time interval. It is shown that the impulsively synchronized chaos can be kept forever if the largest SLLE of error dynamical systems is negative and then the burst behavior will not appear. In addition, the impulsive synchronization with negative SLLE allows large synchronizable impulsive interval, which is significant for applications.

Phase transitions associated with dynamical properties of chaotic systems

1987 ◽  
Vol 36 (7) ◽  
pp. 3525-3528 ◽  
Author(s):  
P. Szépfalusy ◽  
T. Tél ◽  
A. Csordás ◽  
Z. Kovács
Keyword(s):  
Phase Transitions ◽  
Chaotic Systems ◽  
Dynamical Properties

A New Method Based on Lyapunov Exponent to Determine the Threshold of Chaotic Systems

2014 ◽  
Vol 511-512 ◽  
pp. 329-333
Author(s):  
Yang Liu ◽  
Xin Chun Zhang
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic Systems ◽  
Sampling Period ◽  
Qr Decomposition ◽  
Sampling Time ◽  
Duffing Equation ◽  
Experimental Results ◽  
New Method ◽  
Critical Threshold ◽  
Periodic Signals

The Duffing equation has been widely used to detect weak periodic signals. The transition threshold is the key to detect. Unfortunately, there is no effective method to determine the critical threshold. To solve this problem, a new method based on the QR decomposition to calculate Lyapunov exponent is presented. The accuracy of the algorithm will gradually improve with the sampling time increasing or the sampling period decreasing. The experimental results show that the method can determine the interval which contains the threshold, and detect the mutation acts of chaotic systems.

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