Designing a multi-scroll chaotic system by operating Logistic map with fractal process

2017 ◽  
Vol 88 (3) ◽  
pp. 1655-1675 ◽  
Author(s):  
Nabil Ben Slimane ◽  
Kais Bouallegue ◽  
Mohsen Machhout
Keyword(s):  
Chaotic System ◽  
Logistic Map ◽  
Fractal Process

Soft Computing Simulations of Chaotic Systems

2019 ◽  
Vol 29 (08) ◽  
pp. 1950112 ◽  
Author(s):  
Erivelton G. Nepomuceno ◽  
Priscila F. S. Guedes ◽  
Alípio M. Barbosa ◽  
Matjaž Perc ◽  
Robert Repnik
Keyword(s):  
Lower Bound ◽  
Soft Computing ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Logistic Map ◽  
Largest Lyapunov Exponent ◽  
Lower And Upper Bounds ◽  
Finite Precision ◽  
Chua Circuit ◽  
Widespread Interest

Soft computing strategies are drawing widespread interest in engineering and science fields, particularly so because of their capacity to reason and learn in a domain of inherent uncertainty, approximation, and unpredictability. However, soft computing research devoted to finite precision effects in chaotic system simulations is still in a nascent stage, and there are ample opportunities for new discoveries. In this paper, we consider the error that is due to finite precision in the simulation of chaotic systems. We present a generalized version of the lower bound error using an arbitrary number of natural interval extensions. The lower bound error has been used to simulate a chaotic system with lower and upper bounds. The width of this interval does not diverge, which is an advantage compared to other techniques. We illustrate our approach on three systems, namely the logistic map, the Singer map and the Chua circuit. Moreover, we validate the method by calculating the largest Lyapunov exponent.

FPGA REALIZATION OF COMPLEX LOGISTIC MAP FRACTAL BEHAVIOR

Fractals ◽  
2021 ◽  
Author(s):  
BAHAA-ALDEEN M. ABO-ALNAGA ◽  
LOBNA A. SAID ◽  
AHMED H. MADIAN ◽  
AHMED G. RADWAN
Keyword(s):  
Chaotic System ◽  
Mathematical Analysis ◽  
Logistic Map ◽  
Hardware Architecture ◽  
Chaotic Attractors ◽  
Digital Architecture ◽  
Digital Hardware

This paper studies the capability of digital architecture to mimic fractal behavior. As chaotic attractors realized digitally had opened many tracks, digital designs mimicking fractals may ultimately achieve the same. This study is based on a complex single-dimensional discrete chaotic system known as the generalized positive logistic map. The fractals realized from this system are linked to the results of the mathematical analysis to understand the fractal behavior with different variations. A digital hardware architecture manifesting the fractal behavior is achieved on FPGA, showing a fractal entity experimentally. With this digital realization, it is hoped that fractals can follow the example of chaotic attractors digital applications.

Improving the Degradation of Digital Logistic Map via External Control

2014 ◽  
Vol 543-547 ◽  
pp. 1571-1574
Author(s):  
Ya Shuang Deng ◽  
Han Ping Hu
Keyword(s):  
Chaotic System ◽  
Logistic Map ◽  
Modular Function ◽  
Statistical Properties ◽  
External Control ◽  
State Control ◽  
Degradation Problem

In this paper, the degradation problem of digital Logistic map is investigated. Chen chaotic system is applied to anti-control the digital Logistic map and a controller that combines an external state control along with a modular function is designed. Results of the experiments show that the external control can greatly improve the dynamical and statistical properties. Thus, it can be used in cryptography applications.

scholarly journals Novel Method of Secure Communication using Logistic Map

2019 ◽  
Vol 8 (2S7) ◽  
pp. 603-605
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Control Parameter ◽  
Initial Conditions ◽  
Daily Life ◽  
Logistic Map ◽  
New Concepts ◽  
Chaotic Cryptography ◽  
Significant Research ◽  
Novel Method

Significant research efforts have been invested in recent years to export new concepts for secure cryptographic methods. Many mathematicians are attracted by Chaos functions as it has sensitive nature toward its initial conditions and their colossal suitability to problems in daily life. Inspired by new researches, a new chaotic cryptography algorithm is proposed in this paper. The key feature of this approach is that instantaneous key is generated at host independently that is used to determine the type of operations on each pixel. The information available in images is 24 bit RGB these value are modified mathematically using eight reversible operations. Also during encryption, the control parameter of the chaotic system is updated timely.

scholarly journals Study on One Modified Chaotic System Based on Logistic Map

2013 ◽  
Vol 5 (3) ◽  
pp. 898-904 ◽  
Author(s):  
Hua Xue ◽  
Shubin Wang ◽  
Xiandong Meng
Keyword(s):  
Chaotic System ◽  
Logistic Map

A NEW CHAOTIC CRYPTOGRAPHY BASED ON ERGODICITY

2008 ◽  
Vol 22 (07) ◽  
pp. 901-908 ◽  
Author(s):  
XINGYUAN WANG ◽  
CHAOFENG DUAN ◽  
NINI GU
Keyword(s):  
Chaotic System ◽  
Control Parameter ◽  
Chaotic Map ◽  
Logistic Map ◽  
Initial Condition ◽  
Secret Key ◽  
Chaotic Cryptography ◽  
And Diffusion ◽  
Confusion And Diffusion ◽  
Number Of Iterations

This paper analyzes the encryption and weaknesses of E. Álvarez cryptography. On the basis of this, a new chaotic cryptography based on ergodicity is presented. The control parameter and the initial condition of the chaotic system are chosen as a secret key. A bit chain is generated by iterating the chaotic map, and the location where a plaintext grouping appears in the chain is found. We then write down the number of iterations of the chaotic map as the ciphertext grouping. Several weaknesses of the E. Álvarez cryptography are avoided in the new scheme, and the security of the new scheme is improved. In the end, the new cryptography is studied experimentally using the Logistic map, where the new cryptography's confusion and diffusion is validated, and its effectiveness is also illuminated.

scholarly journals Spatiotemporal chaos in Arnold coupled logistic map lattice

2013 ◽  
Vol 18 (4) ◽  
pp. 526-541 ◽  
Author(s):  
Ying-Qian Zhang ◽  
Xing-Yuan Wang
Keyword(s):  
Mutual Information ◽  
Numerical Simulations ◽  
Bifurcation Diagram ◽  
Chaotic System ◽  
Logistic Map ◽  
Entropy Density ◽  
Spatiotemporal Chaos ◽  
Spatiotemporal Dynamics ◽  
Coupling Method ◽  
Coupled Map Lattices

In this paper, we propose a new spatiotemporal dynamics of Arnold coupled logistic map lattice (ACLML). Here, the coupling method between lattices is not a neighborhood coupling but the non-neighborhood of Arnold cat maps. In the proposed system, the criteria such as Kolmogorov–Sinai entropy density and universality, bifurcation diagram, mutual information, space amplitude and space-time diagrams are investigated in this paper. The new features of the proposed system include the lower mutual information between lattices, larger range of parameters for chaotic behaviors, the higher percentage of lattices in chaotic behaviors for most of parameters and less periodic window in bifurcation diagram. These features are more suitable for cryptography. For numerical simulations, we have employed the coupled map lattices system (CML) for comparison. The results indicate that the proposed system has those superior features to the coupled map lattice system (CML). It should be highlighted that the proposed ACLML is a suitable chaotic system for cryptography.

scholarly journals A New Parallel Fuzzy Multi Modular Chaotic Logistic Map for Image Encryption

2021 ◽  
Vol 18 (2) ◽  
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Random Number Generator ◽  
Security Analysis ◽  
Dynamic Parameter ◽  
Randomization Test ◽  
Test Results ◽  
Chaotic Logistic Map

This paper introduces a new image encryption algorithm based on a Parallel Fuzzy Multi-Modular Chaotic Logistic Map (PFMM-CLM). Firstly, a new hybrid chaotic system is introduced by using four parallel cascade chaotic logistic maps with a dynamic parameter control to achieve a high Lyapunov exponent value and completely chaotic behavior of the bifurcation diagram. Also, the fuzzy set theory is used as a fuzzy logic selector to improve chaotic performance. The proposed algorithm has been tested as a Pseudo-Random Number Generator (PRNG). The randomness test results indicate that system has better performance and satisfied all random tests. Finally, the Arnold Cat Map with controllable iterative parameters is used to enhance the confusion concept. Due to excellent chaotic properties and good randomization test results, the proposed chaotic system is used in image encryption applications. The simulation and security analysis indicate that this proposed algorithm has a very high security performance and complexity

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