Maximum entropy approximation for Lyapunov exponents of chaotic maps

2002 ◽  
Vol 43 (5) ◽  
pp. 2518 ◽  
Author(s):  
Jiu Ding ◽  
Lawrence R. Mead
Keyword(s):  
Maximum Entropy ◽  
Lyapunov Exponents ◽  
Chaotic Maps

Two Simplest Quadratic Chaotic Maps Without Equilibrium

2018 ◽  
Vol 28 (12) ◽  
pp. 1850144 ◽  
Author(s):  
Shirin Panahi ◽  
Julien C. Sprott ◽  
Sajad Jafari
Keyword(s):  
Dynamical System ◽  
Bifurcation Diagram ◽  
Lyapunov Exponents ◽  
Chaotic Maps ◽  
Basin Of Attraction ◽  
Hidden Attractor ◽  
Return Map ◽  
Right Hand ◽  
Dynamical Properties ◽  
The Right

Two simple chaotic maps without equilibria are proposed in this paper. All nonlinearities are quadratic and the functions of the right-hand side of the equations are continuous. The procedure of their design is explained and their dynamical properties such as return map, bifurcation diagram, Lyapunov exponents, and basin of attraction are investigated. These maps belong to the hidden attractor category which is a newly introduced category of dynamical system.

Lyapunov exponents of a lattice of chaotic maps with a power-law coupling

2001 ◽  
Vol 286 (2-3) ◽  
pp. 134-140 ◽  
Author(s):  
Antônio M. Batista ◽  
Ricardo L. Viana
Keyword(s):  
Lyapunov Exponents ◽  
Power Law ◽  
Chaotic Maps

scholarly journals A Nonlinearly Modulated Logistic Map With Delay for Image Encryption

Electronics ◽  
2018 ◽  
Vol 7 (11) ◽  
pp. 326 ◽  
Author(s):  
Shouliang Li ◽  
Benshun Yin ◽  
Weikang Ding ◽  
Tongfeng Zhang ◽  
Yide Ma
Keyword(s):  
Lyapunov Exponents ◽  
Image Encryption ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Logistic Map ◽  
Delay Model ◽  
Test Results ◽  
Bit Plane ◽  
Differential Attacks ◽  
Image Encryption Algorithm

Considering that a majority of the traditional one-dimensional discrete chaotic maps have disadvantages including a relatively narrow chaotic range, smaller Lyapunov exponents, and excessive periodic windows, a new nonlinearly modulated Logistic map with delay model (NMLD) is proposed. Accordingly, a chaotic map called a first-order Feigenbaum-Logistic NMLD (FL-NMLD) is proposed. Simulation results demonstrate that FL-NMLD has a considerably wider chaotic range, larger Lyapunov exponents, and superior ergodicity compared with existing chaotic maps. Based on FL-NMLD, we propose a new image encryption algorithm that joins the pixel plane and bit-plane shuffle (JPB). The simulation and test results confirm that JPB has higher security than simple pixel-plane encryption and is faster than simple bit-plane encryption. Moreover, it can resist the majority of attacks including statistical and differential attacks.

scholarly journals On Two-Dimensional Fractional Chaotic Maps with Symmetries

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 756 ◽  
Author(s):  
Fatima Hadjabi ◽  
Adel Ouannas ◽  
Nabil Shawagfeh ◽  
Amina-Aicha Khennaoui ◽  
Giuseppe Grassi
Keyword(s):  
Fixed Points ◽  
Lyapunov Exponents ◽  
Chaotic Maps ◽  
Chaotic Behavior ◽  
Closed Curve ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Coexisting Attractors

In this paper, we propose two new two-dimensional chaotic maps with closed curve fixed points. The chaotic behavior of the two maps is analyzed by the 0–1 test, and explored numerically using Lyapunov exponents and bifurcation diagrams. It has been found that chaos exists in both fractional maps. In addition, result shows that the proposed fractional maps shows the property of coexisting attractors.

LYAPUNOV SPECTRA OF COUPLED CHAOTIC MAPS

2008 ◽  
Vol 18 (12) ◽  
pp. 3759-3770
Author(s):  
XIAOWEN LI ◽  
YU XUE ◽  
PENGLIANG SHI ◽  
GANG HU
Keyword(s):  
Lyapunov Exponents ◽  
Coupling Strength ◽  
Chaotic Maps ◽  
System Size ◽  
Scaling Exponent ◽  
Parameter Region ◽  
Lyapunov Spectra ◽  
Scaling Region ◽  
Model Independent ◽  
Largest Lyapunov Exponents

Largest Lyapunov exponents and Lyapunov spectra of desynchronous coupled chaotic maps with finite coupling strength are investigated by considering different map functions. For sufficiently large system size there exists a parameter region where the largest Lyapunov exponents are independent of system size and coupling strength. This parameter region is called the scaling region. Some scaling exponent and scaling function in the distribution of Lyapunov spectra are found. These scaling behaviors are model independent. All the above numerical observations are explained, based on heuristic physical understanding of the competition of intensity of chaoticity, and strength of coupling, and on an analogy of the discrete coupled maps with continuous extended systems.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

Lyapunov Exponents

2016 ◽  
Author(s):  
Arkady Pikovsky ◽  
Antonio Politi
Keyword(s):  
Lyapunov Exponents
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