Universal Behavior of the Convergence to the Stationary State for a Tangent Bifurcation in the Logistic Map

2020 ◽  
Vol 9 (1) ◽  
pp. 63-70
Author(s):  
Joelson D. V. Hermes ◽  
Fl´avio Heleno Graciano ◽  
Edson D. Leonel
Keyword(s):  
Stationary State ◽  
Logistic Map ◽  
Universal Behavior ◽  
Tangent Bifurcation

SUNSPOT ACTIVITY CURVES AND INTERMITTENT CHAOTIC BEHAVIOR

1995 ◽  
Vol 05 (04) ◽  
pp. 1213-1219
Author(s):  
GÜLŞEN GÜRBÜZ ◽  
CHRISTIAN BECK
Keyword(s):  
Chaotic Behavior ◽  
Logistic Map ◽  
Maunder Minimum ◽  
Sunspot Activity ◽  
Characteristic Numbers ◽  
Injection Model ◽  
Tangent Bifurcation ◽  
Low Dimensional ◽  
Grand Minima

We analyze the statistical properties of observed sunspot numbers. Near the Maunder minimum, the dynamics of successive sunspot maxima is low-dimensional and has properties similar to the intermittent logistic map. The long-term statistics is well described by an intermittent random injection model with Poissonian injection statistics. Three different characteristic numbers are extracted from the solar signal: The distance from the critical point of tangent bifurcation, the injection probability into the laminar phase, and the relaxation time of correlations. It is suggested to interpret the grand minima of the solar cycle as the laminar phase of the intermittent solar dynamo.

scholarly journals LYAPUNOV EXPONENTS FOR THE INTERMITTENT TRANSITION TO CHAOS

1999 ◽  
Vol 09 (04) ◽  
pp. 657-670
Author(s):  
JAMES HANSSEN ◽  
WALTER WILCOX
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Single Channel ◽  
Logistic Map ◽  
Transition To Chaos ◽  
Tangent Bifurcation ◽  
Discrete Nature ◽  
Improved Model ◽  
Modified Theory ◽  
Full Simulation

The dependence of the Lyapunov exponent on the closeness parameter, ε, in tangent bifurcation systems is investigated. We study and illustrate two averaging procedures for defining Lyapunov exponents in such systems. First, we develop theoretical expressions for an isolated tangency channel in which the Lyapunov exponent is defined on single channel passes. Numerical simulations were done to compare theory to measurement across a range of ε values. Next, as an illustration of defining the Lyapunov exponent on many channel passes, a simulation of the intermittent transition in the logistic map is described. The modified theory for the channels is explained and a simple model for the gate entrance rates is constructed. An important correction due to the discrete nature of the iterative flow is identified and incorporated in an improved model. Realistic fits to the data were made for the Lyapunov exponents from the logistic gate and from the full simulation. A number of additional corrections which could improve the treatment of the gates are identified and briefly discussed.

scholarly journals CONVERGENCE TO THE CRITICAL ATTRACTOR AT INFINITE AND TANGENT BIFURCATION POINTS

2006 ◽  
Vol 16 (08) ◽  
pp. 2369-2375
Author(s):  
R. TONELLI
Keyword(s):  
Phase Space ◽  
Lyapunov Exponent ◽  
Numerical Experiment ◽  
Power Law ◽  
Initial Conditions ◽  
Logistic Map ◽  
Nonextensive Statistical Mechanics ◽  
Bifurcation Points ◽  
Tangent Bifurcation ◽  
Set Up

The dynamics of the convergence to the critical attractor for the logistic map is investigated. At the border of chaos, when the Lyapunov exponent is zero, the use of the nonextensive statistical mechanics formalism allows to define a weak sensitivity or insensitivity to initial conditions. Using this formalism we analyze how a set of initial conditions spread all over the phase space converges to the critical attractor in the case of infinite bifurcation and tangent bifurcation points. We show that the phenomena is governed in both cases by a power-law regime but the critical exponents depend on the type of bifurcation and may also depend on the numerical experiment set-up. Differences and similarities between the two cases are also discussed.

School-Wide Universal Behavior Sustainability Index–School Teams

2009 ◽  
Author(s):  
K. McIntosh ◽  
J. D. Doolittle ◽  
C. G. Vincent ◽  
R. H. Horner ◽  
R. A. Ervin
Keyword(s):  
Universal Behavior ◽  
Sustainability Index

Image Encryption Algorithm Based on Substitution Principle and Shuffling Scheme

2020 ◽  
Vol 38 (3B) ◽  
pp. 98-103
Author(s):  
Atyaf S. Hamad ◽  
Alaa K. Farhan
Keyword(s):  
Image Encryption ◽  
Chaotic Map ◽  
Logistic Map ◽  
Encryption Algorithm ◽  
Second Phase ◽  
Cipher Text ◽  
The Face ◽  
Substitution Principle ◽  
2D Logistic Map ◽  
Image Encryption Algorithm

This research presents a method of image encryption that has been designed based on the algorithm of complete shuffling, transformation of substitution box, and predicated image crypto-system. This proposed algorithm presents extra confusion in the first phase because of including an S-box based on using substitution by AES algorithm in encryption and its inverse in Decryption. In the second phase, shifting and rotation were used based on secrete key in each channel depending on the result from the chaotic map, 2D logistic map and the output was processed and used for the encryption algorithm. It is known from earlier studies that simple encryption of images based on the scheme of shuffling is insecure in the face of chosen cipher text attacks. Later, an extended algorithm has been projected. This algorithm performs well against chosen cipher text attacks. In addition, the proposed approach was analyzed for NPCR, UACI (Unified Average Changing Intensity), and Entropy analysis for determining its strength.

Chaotic logistic map, parabola, and gravity

2019 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Logistic Map ◽  
Chaotic Logistic Map

I am trying to connect gravity with chaos via the parabola in the logistic map.

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