scholarly journals On computing the Lyapunov exponents of reversible cellular automata

2020 ◽  
Author(s):  
Johan Kopra
Keyword(s):  
Lyapunov Exponent ◽  
Cellular Automata ◽  
Lyapunov Exponents ◽  
Rational Number ◽  
Absolute Constant ◽  
Uniform Measure ◽  
Positive Rational Number ◽  
Reversible Cellular Automata

AbstractWe consider the problem of computing the Lyapunov exponents of reversible cellular automata (CA). We show that the class of reversible CA with right Lyapunov exponent 2 cannot be separated algorithmically from the class of reversible CA whose right Lyapunov exponents are at most $$2-\delta$$ 2 - δ for some absolute constant $$\delta >0$$ δ > 0 . Therefore there is no algorithm that, given as an input a description of an arbitrary reversible CA F and a positive rational number $$\epsilon >0$$ ϵ > 0 , outputs the Lyapunov exponents of F with accuracy $$\epsilon$$ ϵ . We also compute the average Lyapunov exponents (with respect to the uniform measure) of the reversible CA that perform multiplication by p in base pq for coprime $$p,q>1$$ p , q > 1 .

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

Moment Lyapunov Exponents of a Two-Dimensional Viscoelastic System Under Bounded Noise Excitation

2002 ◽  
Vol 69 (3) ◽  
pp. 346-357 ◽  
Author(s):  
W.-C. Xie
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Two Dimensional ◽  
Bounded Noise ◽  
Regular Perturbation ◽  
Stochastic Fluctuation ◽  
Viscoelastic System ◽  
Moment Lyapunov Exponent ◽  
The Moment ◽  
Moment Lyapunov Exponents

The moment Lyapunov exponents of a two-dimensional viscoelastic system under bounded noise excitation are studied in this paper. An example of this system is the transverse vibration of a viscoelastic column under the excitation of stochastic axial compressive load. The stochastic parametric excitation is modeled as a bounded noise process, which is a realistic model of stochastic fluctuation in engineering applications. The moment Lyapunov exponent of the system is given by the eigenvalue of an eigenvalue problem. The method of regular perturbation is applied to obtain weak noise expansions of the moment Lyapunov exponent, Lyapunov exponent, and stability index in terms of the small fluctuation parameter. The results obtained are compared with those for which the effect of viscoelasticity is not considered.

Reversible cellular automata with memory of delay type

Complexity ◽  
2014 ◽  
Vol 20 (1) ◽  
pp. 49-56 ◽  
Author(s):  
Ramón Alonso-Sanz
Keyword(s):  
Cellular Automata ◽  
Reversible Cellular Automata ◽  
With Memory

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.

Experimental and Simulation of a Cam and Translated Roller Follower Over a Range of Speeds

2016 ◽  
Author(s):  
Louay S. Yousuf ◽  
Dan B. Marghitu
Keyword(s):  
Experimental Data ◽  
Lyapunov Exponent ◽  
High Resolution ◽  
Lyapunov Exponents ◽  
Planar Motion ◽  
Largest Lyapunov Exponents ◽  
Set Up ◽  
The Impact ◽  
Impact With Friction

In this study a cam and follower mechanism is analyzed. There is a clearance between the follower and the guide. The mechanism is analyzed using SolidWorks simulations taking into account the impact and the friction between the roller follower and the guide. Four different follower guide’s clearances have been used in the simulations like 0.5, 1, 1.5, and 2 mm. An experimental set up is developed to capture the general planar motion of the cam and follower. The measures of the cam and the follower positions are obtained through high-resolution optical encoders (markers). The effect of follower guide’s clearance is investigated for different cam rotational speeds such as 100, 200, 300, 400, 500, 600, 700 and 800 R.P.M. Impact with friction is considered in our study to calculate the Lyapunov exponent. The largest Lyapunov exponents for the simulated and experimental data are analyzed and selected.

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