Sufficient condition for chaotic maps to yield chaotic behavior after FM

2008 ◽  
Vol 44 (3) ◽  
pp. 1240-1248 ◽  
Author(s):  
A. Ashtari ◽  
G. Thomas ◽  
W. Kinsner ◽  
B.C. Flores
Keyword(s):  
Chaotic Maps ◽  
Chaotic Behavior ◽  
Sufficient Condition

A Dynamic Duopoly Game with Content Providers’ Bounded Rationality

2020 ◽  
Vol 30 (07) ◽  
pp. 2050095 ◽  
Author(s):  
Hamid Garmani ◽  
Driss Ait Omar ◽  
Mohamed El Amrani ◽  
Mohamed Baslam ◽  
Mostafa Jourhmane
Keyword(s):  
Bounded Rationality ◽  
Chaotic Behavior ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Pricing Decisions ◽  
Dynamical Behaviors ◽  
Duopoly Model ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Dynamic Duopoly

This paper investigates the dynamical behaviors of a duopoly model with two content providers (CPs). Competition between two CPs is assumed to take place in terms of their pricing decisions and the credibility of content they offer. According to the CPs’ rationality level, we consider a scenario where both CPs are bounded rational. Each CP in any period uses the marginal profit observed from the previous period to choose its strategies. We compute explicitly the steady states of the dynamical system induced by bounded rationality, and establish a necessary and sufficient condition for stability of its Nash equilibrium (NE). Numerical simulations show that if some parameters of the model are varied, the stability of the NE point is lost and the complex (periodic or chaotic) behavior occurs. The chaotic behavior of the system is stabilized on the NE point by applying control.

Design and FPGA Implementation of New Multidimensional Chaotic Map for Secure Communication

2021 ◽  
pp. 2150280
Author(s):  
Belqassim Bouteghrine ◽  
Camel Tanougast ◽  
Said Sadoudi
Keyword(s):  
Secure Communication ◽  
Chaotic Systems ◽  
Chaotic Maps ◽  
Chaotic Behavior ◽  
Chaotic Map ◽  
Two Phase ◽  
Multiple Parameters ◽  
Random Keys ◽  
Field Programmable ◽  
Constrained Devices

Due to their structure and complexity, chaotic systems have been introduced in several domains such as electronic circuits, commerce domain, encryption and network security. In this paper, we propose a novel multidimensional chaotic system with multiple parameters and nonlinear terms. Then, a two-phase algorithm is presented for investigating the chaotic behavior using bifurcation and Lyapunov exponent (LE) theories. Finally, we illustrate the performances of our proposal by constructing three (03) chaotic maps (3-D, 4-D and 5-D) and implementing the 3-D map on Field-Programmable-Gate-Array (FPGA) boards to generate random keys for securing a client–server communication purpose. Based on the achieved results, the proposed scheme is considered an ideal candidate for numerous resource-constrained devices and internet of the things (IoT) applications.

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.

scholarly journals GENERATION OF VALUES FROM DISCRETE PROBABILITY DISTRIBUTIONS WITH THE USE OF CHAOTIC MAPS

2020 ◽  
pp. 49-54
Author(s):  
Marcin Lawnik ◽  
Arkadiusz Banasik ◽  
Adrian Kapczyński
Keyword(s):  
Chaotic Maps ◽  
Chaotic Behavior ◽  
Probability Distributions ◽  
Discrete Dynamical System ◽  
Chaotic Map ◽  
Random Variables ◽  
Discrete Distribution ◽  
Random Variable ◽  
Discrete Probability ◽  
Discrete Probability Distributions

The values of random variables are commonly used in the field of artificial intelligence. The literature shows plenty of methods, which allows us to generate them, for example, inverse cumulative density function method. Some of the ways are based on chaotic projection. The chaotic methods of generating random variables are concerned with mainly continuous random variables. This article presents the method of generating values from discrete probability distributions with the use of properly constructed piece-wise linear chaotic map. This method is based on a properly constructed discrete dynamical system with chaotic behavior. Successive probability values cover the unit interval and the corresponding random variable values are assigned to the determined subintervals. In the next step, a piece-wise linear map on the subintervals is constructed. In the course of iterations of the chaotic map, consecutive values from a given discrete distribution are derived. The method is presented on the example of Bernoulli distribution. Furthermore, an analysis of the discussed example is conducted and shows that the presented method is the fastest of all analyzed methods.

A novel parallel chaotic system with greatly improved Lyapunov exponent and chaotic range

2020 ◽  
Vol 34 (07) ◽  
pp. 2050048
Author(s):  
Minghao Zhu ◽  
Chunhua Wang
Keyword(s):  
Performance Evaluation ◽  
Lyapunov Exponent ◽  
Chaotic System ◽  
Parameter Space ◽  
Simple Structure ◽  
Chaotic Maps ◽  
Chaotic Behavior ◽  
The Novel ◽  
Time Performance ◽  
System A

Lyapunov exponent (LE), chaotic range and complexity are the key considerations of a discrete chaotic system. A dynamic chaotic system with larger LE and wider parameter space will result in better statistical performance that can be used to generate pseudo random sequences and applied to encryption fields. At the same time, the combination of simple chaotic maps can generate more excellent chaotic behavior. This paper proposes a newly combined chaotic system called Parallel Chaotic System (PCS). Multiple simple chaotic maps are paralleled to construct the novel system. In this system, LE and chaotic range can be improved as much as possible by setting additional parameters. Compared with the existing models made up of same seed maps, PCS is able to get better chaotic behavior by means of a simple structure at the same time. Performance evaluation emphasizes that the chaotic maps generated by PCS are more unpredictable with better complexity.

scholarly journals PDϑControl Strategy for a Fractional-Order Chaotic Financial Model

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Changjin Xu ◽  
Maoxin Liao ◽  
Peiluan Li ◽  
Qimei Xiao ◽  
Shuai Yuan
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Chaotic Behavior ◽  
Sufficient Condition ◽  
Bifurcation Parameter ◽  
Economic Stability ◽  
Financial Model ◽  
The Stability

In this article, based on the previous works, a new fractional-order financial model is put up. The chaotic behavior of the fractional-order financial model is suppressed by designing an appropriatePDϑcontroller. By choosing the delay as the bifurcation parameter, we establish the sufficient condition to guarantee the stability and the existence of Hopf bifurcation of fractional-order financial model. Also, the influence of the delay and the fractional order on the stability and the existence of Hopf bifurcation of fractional-order financial model is revealed. An example is given to confirm the effectiveness of the analysis results. The main findings of this article play an important role in maintaining economic stability.

scholarly journals A Novel Intermittent Jumping Coupled Map Lattice Based on Multiple Chaotic Maps

2021 ◽  
Vol 11 (9) ◽  
pp. 3797
Author(s):  
Rong Huang ◽  
Fang Han ◽  
Xiaojuan Liao ◽  
Zhijie Wang ◽  
Aihua Dong
Keyword(s):  
Parameter Space ◽  
Random Number ◽  
Chaotic Maps ◽  
Chaotic Behavior ◽  
Random Number Generator ◽  
Coupled Map Lattice ◽  
Number Generator ◽  
Multiple Chaotic Maps ◽  
Image Cryptosystem ◽  
Pseudo Random Number Generator

Coupled Map Lattice (CML) usually serves as a pseudo-random number generator for encrypting digital images. Based on our analysis, the existing CML-based systems still suffer from problems like limited parameter space and local chaotic behavior. In this paper, we propose a novel intermittent jumping CML system based on multiple chaotic maps. The intermittent jumping mechanism seeks to incorporate the multi-chaos, and to dynamically switch coupling states and coupling relations, varying with spatiotemporal indices. Extensive numerical simulations and comparative studies demonstrate that, compared with the existing CML-based systems, the proposed system has a larger parameter space, better chaotic behavior, and comparable computational complexity. These results highlight the potential of our proposal for deployment into an image cryptosystem.

scholarly journals A Novel Audio Cryptosystem Using Chaotic Maps and DNA Encoding

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
S. J. Sheela ◽  
K. V. Suresh ◽  
Deepaknath Tandur
Keyword(s):  
Deoxyribonucleic Acid ◽  
Chaotic Maps ◽  
Chaotic Behavior ◽  
Dna Encoding ◽  
Radio Communication ◽  
Security Applications ◽  
Comparison Results ◽  
Good Potential ◽  
Encryption Decryption ◽  
Cryptographic Attacks

Chaotic maps have good potential in security applications due to their inherent characteristics relevant to cryptography. This paper introduces a new audio cryptosystem based on chaotic maps, hybrid chaotic shift transform (HCST), and deoxyribonucleic acid (DNA) encoding rules. The scheme uses chaotic maps such as two-dimensional modified Henon map (2D-MHM) and standard map. The 2D-MHM which has sophisticated chaotic behavior for an extensive range of control parameters is used to perform HCST. DNA encoding technology is used as an auxiliary tool which enhances the security of the cryptosystem. The performance of the algorithm is evaluated for various speech signals using different encryption/decryption quality metrics. The simulation and comparison results show that the algorithm can achieve good encryption results and is able to resist several cryptographic attacks. The various types of analysis revealed that the algorithm is suitable for narrow band radio communication and real-time speech encryption applications.

The Current Situation in Chemical Stabilization of Biological Materials

1972 ◽  
Vol 30 ◽  
pp. 132-133
Author(s):  
John H. Luft
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Osmium Tetroxide ◽  
Molecular Level ◽  
Cross Linking ◽  
Chemical Stabilization ◽  
Specimen Preparation ◽  
Sufficient Condition ◽  
Radio Telescopes

With information processing devices such as radio telescopes, microscopes or hi-fi systems, the quality of the output often is limited by distortion or noise introduced at the input stage of the device. This analogy can be extended usefully to specimen preparation for the electron microscope; fixation, which initiates the processing sequence, is the single most important step and, unfortunately, is the least well understood. Although there is an abundance of fixation mixtures recommended in the light microscopy literature, osmium tetroxide and glutaraldehyde are favored for electron microscopy. These fixatives react vigorously with proteins at the molecular level. There is clear evidence for the cross-linking of proteins both by osmium tetroxide and glutaraldehyde and cross-linking may be a necessary if not sufficient condition to define fixatives as a class.

Sign in / Sign up

Export Citation Format

Share Document