Loewner Evolution Driven by One-dimensional Chaotic Maps

2020 ◽  
Vol 89 (5) ◽  
pp. 054801 ◽  
Author(s):  
Yusuke Shibasaki ◽  
Minoru Saito
Keyword(s):  
Chaotic Maps ◽  
One Dimensional ◽  
Loewner Evolution

A WEIGHTED CHAOTIC BLOCK ENCRYPTION ALGORITHM USING MULTIPLE ONE-DIMENSIONAL CHAOTIC MAPS

2011 ◽  
Vol 25 (29) ◽  
pp. 3987-3996
Author(s):  
XING-YUAN WANG ◽  
XIAO-JUAN WANG
Keyword(s):  
Chaotic Maps ◽  
Encryption Algorithm ◽  
One Dimensional ◽  
Chaotic Iterations ◽  
Block Encryption

This paper proposes a new block encryption algorithm. The chaotic trajectories are computed by weighting. Then the result is used to mask the plaintext. Multiple blocks of plaintext are encrypted at the same time and this decreases the chaotic iterations. So the encryption speed is improved to some extent. The proposed algorithm is flexible. When the number of weights is increased, the number of the encrypted plaintext block at the same time is increased and the encryption speed is improved. The simulation result shows that the proposed algorithm has fast encryption speed and fine security.

scholarly journals Research on Pseudorandom Number Generator Based on Several New Types of Piecewise Chaotic Maps

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Hongyan Zang ◽  
Yue Yuan ◽  
Xinyuan Wei
Keyword(s):  
Theoretical Basis ◽  
Chaotic Maps ◽  
Dynamic Properties ◽  
Chaotic Map ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
Number Generator ◽  
High Quality ◽  
One Dimensional ◽  
Construction Methods

This paper proposes three types of one-dimensional piecewise chaotic maps and two types of symmetrical piecewise chaotic maps and presents five theorems. Furthermore, some examples that satisfy the theorems are constructed, and an analysis and model of the dynamic properties are discussed. The construction methods proposed in this paper have a certain generality and provide a theoretical basis for constructing a new discrete chaotic system. In addition, this paper designs a pseudorandom number generator based on piecewise chaotic map and studies its application in cryptography. Performance evaluation shows that the generator can generate high quality random sequences efficiently.

STABILIZATION OF CHAOTIC DYNAMICS OF ONE-DIMENSIONAL MAPS BY A CYCLIC PARAMETRIC TRANSFORMATION

1996 ◽  
Vol 06 (04) ◽  
pp. 725-735 ◽  
Author(s):  
ALEXANDER Yu. LOSKUTOV ◽  
VALERY M. TERESHKO ◽  
KONSTANTIN A. VASILIEV
Keyword(s):  
Periodic Orbits ◽  
Chaotic Dynamics ◽  
Chaotic Maps ◽  
Logistic Map ◽  
Exponential Map ◽  
One Dimensional ◽  
Stable Periodic ◽  
One Dimensional Maps ◽  
Parameter Values ◽  
Parametric Transformation

We consider one-dimensional maps, the logistic map and an exponential map, in those sets of parameter values which correspond to their chaotic dynamics. It is proven that such dynamics may be stabilized by a certain cyclic parametric transformation operating strictly within the chaotic set. The stabilization is a result of the creation of stable periodic orbits in the initially chaotic maps. The period of these stable orbits is a multiple of the period of the cyclic transformation. It is shown that stabilized behavior cannot be destroyed by a weak noise smearing of the required parameter values. The regions where the behavior stabilization takes place are numerically estimated. Periods of the created stabile periodic orbits are calculated.

A Chaotification model based on sine and cosecant functions for enhancing chaos

2021 ◽  
Author(s):  
Yuqing Li ◽  
Xing He ◽  
Dawen Xia
Keyword(s):  
Fixed Point ◽  
Lyapunov Exponent ◽  
Chaotic Maps ◽  
Dynamic Properties ◽  
Chaotic Map ◽  
Sample Entropy ◽  
One Dimensional ◽  
Model Based ◽  
Chaotic Region ◽  
Definition Of

Chaotic maps with higher chaotic complexity are urgently needed in many application scenarios. This paper proposes a chaotification model based on sine and cosecant functions (CMSC) to improve the dynamic properties of existing chaotic maps. CMSC can generate a new map with higher chaotic complexity by using the existing one-dimensional (1D) chaotic map as a seed map. To discuss the performance of CMSC, the chaos properties of CMSC are analyzed based on the mathematical definition of the Lyapunov exponent (LE). Then, three new maps are generated by applying three classical 1D chaotic maps to CMSC respectively, and the dynamic behaviors of the new maps are analyzed in terms of fixed point, bifurcation diagram, sample entropy (SE), etc. The results of the analysis demonstrate that the new maps have a larger chaotic region and excellent chaotic characteristics.

FAULT TOLERANCE AND DETECTION IN CHAOTIC COMPUTERS

2007 ◽  
Vol 17 (06) ◽  
pp. 1955-1968 ◽  
Author(s):  
MOHAMMAD R. JAHED-MOTLAGH ◽  
BEHNAM KIA ◽  
WILLIAM L. DITTO ◽  
SUDESHNA SINHA
Keyword(s):  
Chaotic Systems ◽  
Chaotic Maps ◽  
Structural Testing ◽  
Testing Time ◽  
Computing Device ◽  
One Dimensional ◽  
Testing Method ◽  
Higher Dimensional ◽  
Parameter Variations ◽  
Logic Blocks

We introduce a structural testing method for a dynamics based computing device. Our scheme detects different physical defects, manifesting themselves as parameter variations in the chaotic system at the core of the logic blocks. Since this testing method exploits the dynamical properties of chaotic systems to detect damaged logic blocks, the damaged elements can be detected by very few testing inputs, leading to very low testing time. Further the method does not entail dedicated or extra hardware for testing. Specifically, we demonstrate the method on one-dimensional unimodal chaotic maps. Some ideas for testing higher dimensional maps and flows are also presented.

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