A study on initial values of the logistic map over integers

2009 ◽  
Author(s):  
Shunsuke Araki ◽  
Takeru Miyazaki ◽  
Satoshi Uehara
Keyword(s):  
Logistic Map ◽  
Initial Values

Difference in the dynamics of logistic maps

2019 ◽  
Vol 33 (20) ◽  
pp. 1950226
Author(s):  
Tianshu Song ◽  
Hui Xia
Keyword(s):  
Logistic Map ◽  
Jigsaw Puzzle ◽  
Initial Values ◽  
The Difference

We investigate the evolution of the difference in the conventional logistic map and observed complicated but interesting dynamics. Our results show that the bifurcation, the attractor and the asymptotic measure depend on initial values. The reverse bifurcation, the multiple bifurcation and other bifurcation properties obtained here are different from those of the original logistic map. Furthermore, we find that attractors form a structure which looks like a jigsaw puzzle, and the corresponding distributions related to the Feigenbaum constant are also analyzed.

THE INFLUENCE OF VITAMIN C ON EOSINOPHIL RESPONSE TO ACUTE ALCOHOL INTOXICATION IN RATS

1960 ◽  
Vol XXXV (IV) ◽  
pp. 585-593 ◽  
Author(s):  
T. P. J. Vanha-Perttula
Keyword(s):  
Vitamin C ◽  
Ethyl Alcohol ◽  
Intraperitoneal Injection ◽  
Alcohol Intoxication ◽  
Albino Rats ◽  
Acute Alcohol Intoxication ◽  
Alcohol Administration ◽  
Initial Values

ABSTRACT The effect of ethyl alcohol on the circulating eosinophil cells has been studied in female albino rats. An intoxicating dose of alcohol caused a marked depletion of circulating eosinophils which was most clearly evident four hours after the administration of the alcohol. The initial values were not reached before 24 hours had elapsed. Intraperitoneal injection of vitamin C 12 hours prior to the alcohol administration very effectively prevented this eosinopenic reaction. The mechanism of regulation of the eosinophil cells in the circulation has been discussed in the light of previous results and of those obtained in this study.

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.

The Role Of The Pilates Method In The Formation And Development Of The Body Balance

2019 ◽  
pp. 78-83
Author(s):  
Irene-Teodora Nica
Keyword(s):  
The Body ◽  
Target Group ◽  
Body Balance ◽  
Initial Values ◽  
Pilates Method

The study is aimed at training and developing balance through Pilates programs. In order to improve the initial values, we have developed a set of corresponding exercises. The test was applied on a target group, the initial and final results being presented. The conclusion presents the interpretation of the results.

Linear and Nonlinear Dynamic Behaviour

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Dynamic Behavior ◽  
Dynamic Systems ◽  
Dynamic Behaviour ◽  
Nonlinear Dynamical Systems ◽  
Logistic Map ◽  
Nonlinear Dynamical ◽  
Deterministic Dynamic ◽  
Random Behavior ◽  
Single Solution ◽  
Equivalent Systems

In this chapter, we describe how highly erratic dynamic behavior can arise from a nonlinear logistic map, and how this apparently random behavior is governed by a surprising order. With this lesson in mind, we should not be overly surprised that highly erratic and random appearing observed data might also be generated by parsimonious deterministic dynamic systems. At a minimum, we contend that researchers should apply NLTS to test for this possibility. We also introduced tools to analyze dynamic behavior that form the foundation for NLTS. In particular, we have stressed the quite unexpected capability to achieve some form of predictability even with only one trajectory at hand. In subsequent chapters, we treat known nonlinear dynamical systems as unknown, and investigate how NLTS methods rely on a single solution (or multiple solutions) generated by them to reconstruct equivalent systems. This is a conventional approach in the literature for seeing how NLTS methods work since we know what needs to be reconstructed.

scholarly journals Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 474 ◽  
Author(s):  
Lazaros Moysis ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Jesus M. Munoz-Pacheco ◽  
Jacques Kengne ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Image Encryption ◽  
Fuzzy Numbers ◽  
Statistical Tests ◽  
Logistic Map ◽  
Simple Rule ◽  
Pseudorandom Number ◽  
Bifurcation Diagrams ◽  
Triangular Numbers ◽  
Pseudorandom Number Generation

A modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis. The map is then applied to the problem of pseudo random bit generation, using a simple rule to generate the bit sequence. The resulting random bit generator (RBG) successfully passes the National Institute of Standards and Technology (NIST) statistical tests, and it is then successfully applied to the problem of image encryption.

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