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.

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.

scholarly journals True Random Number Generation from Bioelectrical and Physical Signals

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Seda Arslan Tuncer ◽  
Turgay Kaya
Keyword(s):  
Blood Volume ◽  
Random Number ◽  
Logistic Map ◽  
Random Number Generation ◽  
Statistical Properties ◽  
Random Numbers ◽  
Number Generation ◽  
Skin Response ◽  
Volume Pulse ◽  
Blood Volume Pulse

It is possible to generate personally identifiable random numbers to be used in some particular applications, such as authentication and key generation. This study presents the true random number generation from bioelectrical signals like EEG, EMG, and EOG and physical signals, such as blood volume pulse, GSR (Galvanic Skin Response), and respiration. The signals used in the random number generation were taken from BNCIHORIZON2020 databases. Random number generation was performed from fifteen different signals (four from EEG, EMG, and EOG and one from respiration, GSR, and blood volume pulse datasets). For this purpose, each signal was first normalized and then sampled. The sampling was achieved by using a nonperiodic and chaotic logistic map. Then, XOR postprocessing was applied to improve the statistical properties of the sampled numbers. NIST SP 800-22 was used to observe the statistical properties of the numbers obtained, the scale index was used to determine the degree of nonperiodicity, and the autocorrelation tests were used to monitor the 0-1 variation of numbers. The numbers produced from bioelectrical and physical signals were successful in all tests. As a result, it has been shown that it is possible to generate personally identifiable real random numbers from both bioelectrical and physical signals.

A DESIGN OF PSEUDO-RANDOM BIT GENERATOR BASED ON SINGLE CHAOTIC SYSTEM

2012 ◽  
Vol 23 (03) ◽  
pp. 1250024 ◽  
Author(s):  
XING-YUAN WANG ◽  
YI-XIN XIE
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Statistical Properties ◽  
Security Issues ◽  
Initial Sensitivity ◽  
Wide Range ◽  
Random Bit Generator ◽  
Dynamical Properties ◽  
Experimental Analyses

Pseudo-random bit sequence have a wide range of applications in the field of cryptography and communications. For the good chaotic dynamical properties of chaotic systems sequence such as randomness and initial sensitivity, chaotic systems have a strong advantage in generating the pseudo-random bit sequence. However, in practical use, the dynamical properties of chaotic systems will be degraded because of the limited calculation accuracy and it even could cause a variety of security issues. To improve the security, in full analyses of the pseudo-random bit generator proposed in our former paper, we point out some problems in our former design and redesign a better pseudo-random bit generator base on it. At the same time, we make some relevant theoretical and experimental analyses on it. The experiments show that the design proposed in this paper has good statistical properties and security features.

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.

Friendly Societies and the Discourse of Respectability in Britain, 1825–1875

1995 ◽  
Vol 34 (1) ◽  
pp. 35-58 ◽  
Author(s):  
Simon Cordery
Keyword(s):  
Middle Class ◽  
Working Class ◽  
Social Power ◽  
External Control ◽  
State Control ◽  
Members Of Parliament ◽  
Self Help ◽  
Ruling Elites ◽  
Class Context ◽  
Friendly Societies

In nineteenth-century Britain, friendly societies (working-class mutual benefit clubs) and ruling elites contested definitions of respectability and independence in a struggle to delineate relations between societies and the state. This process was an important part of an ongoing set of negotiations by which working-class organizations influenced middle-class attitudes toward collective action. Pressure from friendly societies forced members of Parliament and bureaucrats to accept their claim to respectability and, with it, to independence from state control, changing the discourse of respectability in three stages. During the first quarter of the century, clergymen and landowners equated respectability with middle-class patronage and independence from the Poor Law. Around midcentury, the societies appropriated the discourse of respectability and, with qualified elite approval, used it to redefine independence as freedom from middle-class supervision. By the 1870s, however, friendly society leaders requested government assistance to limit the independence of rank-and-file members, whose autonomy they claimed was a threat to the societies' respectability.Friendly societies wanted, as one member wrote, “to do what is ‘respectable.’” This meant redefining respectability in a collective, working-class context. While middle-class definitions rested on the premise that individualism and self-help were the twin foundations of respectability, friendly societies gained access to the social power of respectability by offering an alternative definition based on collective self-help and independence from external control. Friendly societies were democratically managed insurance clubs offering sickness and burial coverage and sociable activities in return for regular payments. They often met in public houses, which they identified as respectable, contradicting middle-class attitudes.

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.

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

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
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