scholarly journals Reliability Modeling and Optimization Using Fuzzy Logic and Chaos Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Alexander Rotshtein ◽  
Denys Katielnikov ◽  
Ludmila Pustylnik
Keyword(s):  
Chaos Theory ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Systems Design ◽  
Membership Functions ◽  
Problem Statement ◽  
Reliability Modeling ◽  
Chaos Generator ◽  
Influencing Parameters ◽  
The Moment

Fuzzy sets membership functions integrated with logistic map as the chaos generator were used to create reliability bifurcations diagrams of the system with redundancy of the components. This paper shows that increasing in the number of redundant components results in a postponement of the moment of the first bifurcation which is considered as most contributing to the loss of the reliability. The increasing of redundancy also provides the shrinkage of the oscillation orbit of the level of the system’s membership to reliable state. The paper includes the problem statement of redundancy optimization under conditions of chaotic behavior of influencing parameters and genetic algorithm of this problem solving. The paper shows the possibility of chaos-tolerant systems design with the required level of reliability.

Chaos in Economics

2014 ◽  
pp. 440-460
Author(s):  
Wei-Bin Zhang
Keyword(s):  
Growth Model ◽  
Chaos Theory ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Economic Models ◽  
Optimal Growth ◽  
Lorenz Equations ◽  
Urban Dynamics ◽  
Long Run ◽  
The One

The paper introduces applications of chaos theory in economics. By studying some economic models which exhibit chaotic behavior both in discrete and continuous times and in different dimensions, this paper demonstrates wide applications of chaos theory in different schools of economics. In particular, the paper argues that chaos theory is a basic tool for integrating various economic theories within a new dynamic theory. The paper first introduces the topic and gives a basic survey of the early literature. Then it examines chaotic behavior of some economic models. Application 1 introduces the logistic map and examines the one-dimensional discrete growth model with population by Haavelmo and Stutzer. Application 2 identifies economic chaos in the disequilibrium inventory model by Hommes. Application 3 studies a long-run competitive two-periodic OLG model with money and capital. Application 4 discusses the Lorenz equations and its application to urban dynamics. Application 5 introduces the traditional optimal growth model with multiple capital goods, demonstrating the existence of periodic and aperiodic solutions. Finally we conclude the study and discuss some implications of chaos theory for creating a general economic theory.

Non-Linearity and Chaotic Behaviour in Cyprus Stock Market

2015 ◽  
Vol 5 (4) ◽  
Author(s):  
Athina Bougioukou
Keyword(s):  
Lyapunov Exponent ◽  
Stock Market ◽  
Chaos Theory ◽  
Linear Dependence ◽  
Chaotic Behavior ◽  
Efficient Market Hypothesis ◽  
Chaotic Behaviour ◽  
Maximum Lyapunov Exponent ◽  
Efficient Market ◽  
General Index

The intention of this research is to investigate the aspect of non-linearity and chaotic behavior of the Cyprus stock market. For this purpose, we use non-linearity and chaos theory. We perform BDS, Hinich-Bispectral tests and compute Lyapunov exponent of the Cyprus General index. The results show that existence of non-linear dependence and chaotic features as the maximum Lyapunov exponent was found to be positive. This study is important because chaos and efficient market hypothesis are mutually exclusive aspects. The efficient market hypothesis which requires returns to be independent and identically distributed (i.i.d.) cannot be accepted.

A case study in bifurcation theory

2017 ◽  
Vol 28 (08) ◽  
pp. 1750104 ◽  
Author(s):  
Youssef Khmou
Keyword(s):  
Dynamical Systems ◽  
Bifurcation Theory ◽  
Chaotic Behavior ◽  
Numerical Study ◽  
Logistic Map ◽  
Logistic Function ◽  
Second Order ◽  
Short Paper ◽  
Chaotic Region

This short paper is focused on the bifurcation theory found in map functions called evolution functions that are used in dynamical systems. The most well-known example of discrete iterative function is the logistic map that puts into evidence bifurcation and chaotic behavior of the topology of the logistic function. We propose a new iterative function based on Lorentizan function and its generalized versions, based on numerical study, it is found that the bifurcation of the Lorentzian function is of second-order where it is characterized by the absence of chaotic region.

scholarly journals Cosmopolitan Sophistry: Grounding Politics in Disorder and Uncertainty

2011 ◽  
Vol 3 (3) ◽  
pp. 197-223
Author(s):  
Jon Marshall
Keyword(s):  
Social Movement ◽  
Chaos Theory ◽  
Evolutionary Ecology ◽  
The State ◽  
Legitimate Authority ◽  
The West ◽  
Social Death ◽  
The Future ◽  
The Moment ◽  
As If

Conceptions of the State, Nation and politics, which are actually in play in ‘the West’, usually descend from totalitarian models which are primarily Platonic and monotheistic in origin. They aim for unity, harmony, wholeness, legitimate authority and the rejection of conflict, however much they claim to represent multiplicity. By expressing a vision of order, such models drive an idea of planning by prophecy as opposed to divination, as if the future was certain within limits and the trajectory was smooth. Chaos theory and evolutionary ecology shows us that this conception of both society and the future is inaccurate. I will argue that it is useful to look at the pre-socratic philosophers, in particular the so-called sophists Gorgias and Protagoras and Heraclitus with their sense of ongoing flux, the truth of the moment, and the necessary power of rhetoric in the leading forth of temporary functional consensus within the flux. This ongoing oscillation of conflict provides social movement and life rather than social death.

An Intrinsically Three-Dimensional Fractal

2014 ◽  
Vol 24 (06) ◽  
pp. 1430017 ◽  
Author(s):  
M. Fernández-Guasti
Keyword(s):  
Bifurcation Diagram ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Three Dimensional ◽  
Periodic Points ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Hyperbolic Numbers ◽  
Self Similar ◽  
One To One

The quadratic iteration is mapped using a nondistributive real scator algebra in three dimensions. The bound set S has a rich fractal-like boundary. Periodic points on the scalar axis are necessarily surrounded by off axis divergent magnitude points. There is a one-to-one correspondence of this set with the bifurcation diagram of the logistic map. The three-dimensional S set exhibits self-similar 3D copies of the elementary fractal along the negative scalar axis. These 3D copies correspond to the windows amid the chaotic behavior of the logistic map. Nonetheless, the two-dimensional projection becomes identical to the nonfractal quadratic iteration produced with hyperbolic numbers. Two- and three-dimensional renderings are presented to explore some of the features of this set.

scholarly journals Neural Network for Low-Memory IoT Devices and MNIST Image Recognition Using Kernels Based on Logistic Map

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1432
Author(s):  
Andrei Velichko
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Classification Accuracy ◽  
Network Architecture ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Simple Algorithm ◽  
Research Perspective ◽  
Logistic Mapping ◽  
Iot Devices

This study presents a neural network which uses filters based on logistic mapping (LogNNet). LogNNet has a feedforward network structure, but possesses the properties of reservoir neural networks. The input weight matrix, set by a recurrent logistic mapping, forms the kernels that transform the input space to the higher-dimensional feature space. The most effective recognition of a handwritten digit from MNIST-10 occurs under chaotic behavior of the logistic map. The correlation of classification accuracy with the value of the Lyapunov exponent was obtained. An advantage of LogNNet implementation on IoT devices is the significant savings in memory used. At the same time, LogNNet has a simple algorithm and performance indicators comparable to those of the best resource-efficient algorithms available at the moment. The presented network architecture uses an array of weights with a total memory size from 1 to 29 kB and achieves a classification accuracy of 80.3–96.3%. Memory is saved due to the processor, which sequentially calculates the required weight coefficients during the network operation using the analytical equation of the logistic mapping. The proposed neural network can be used in implementations of artificial intelligence based on constrained devices with limited memory, which are integral blocks for creating ambient intelligence in modern IoT environments. From a research perspective, LogNNet can contribute to the understanding of the fundamental issues of the influence of chaos on the behavior of reservoir-type neural networks.

A Hierarchical Fuzzy-Neural Multi-Model Applied in Nonlinear Systems Identification and Control

2013 ◽  
Vol 347-350 ◽  
pp. 617-622
Author(s):  
Feng Ye ◽  
Wei Min Qi
Keyword(s):  
Neural Network ◽  
Control System ◽  
Recurrent Neural Network ◽  
Systems Design ◽  
Membership Functions ◽  
Neural Network Models ◽  
Trajectory Tracking Control ◽  
Fuzzy Neural ◽  
Systems Identification ◽  
And Control

The paper brings forward a hierarchical fuzzy-neural multi-model with recurrent neural procedural consequent par for systems identification, states estimation and adaptive control of complex nonlinear plants. The parameters and states of the local recurrent neural network models are used for a local direct and indirect adaptive trajectory tracking control systems design. The designed local control laws are coordinated by a fuzzy rule-based control system. The upper level defuzzyfication is performed by a recurrent neural network. The applicability of the proposed intelligent control system is confirmed by simulation examples and by a DC-motor identification and control experimental results. Two main cases of a reference and plant output fuzzyfication are considereda two membership functions without overlapping and a three membership functions with overlapping. In both cases a good convergent results are obtained.

scholarly journals Deterministic Chaos and Fractal Complexity in the Dynamics of Cardiovascular Behavior: Perspectives on a New Frontier

2009 ◽  
Vol 3 (1) ◽  
pp. 110-123 ◽  
Author(s):  
Vijay Sharma
Keyword(s):  
Cardiovascular System ◽  
Chaos Theory ◽  
Fractal Structure ◽  
Chaotic Behavior ◽  
Heart Function ◽  
Deterministic Chaos ◽  
Physical Structure ◽  
Cellular Level ◽  
Mathematical Concepts ◽  
Evolutionary Origins

Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts.

Biometric Template Protection Using Spiral Cube: Performance and Security Analysis

2016 ◽  
Vol 25 (01) ◽  
pp. 1550027 ◽  
Author(s):  
Chouaib Moujahdi ◽  
George Bebis ◽  
Sanaa Ghouzali ◽  
Mounia Mikram ◽  
Mohammed Rziza
Keyword(s):  
Chaotic Behavior ◽  
Logistic Map ◽  
Security Analysis ◽  
Personal Data ◽  
Random Projection ◽  
Biometric Template ◽  
Template Protection ◽  
And Performance ◽  
Biometric Templates ◽  
Biometric Template Protection

Personal authentication systems based on biometrics have given rise to new problems and challenges related to the protection of personal data, issues of less concern in traditional authentication systems. The irrevocability of biometric templates makes biometric systems very vulnerable to several attacks. In this paper we present a new approach for biometric template protection. Our objective is to build a non-invertible transformation, based on random projection, which meets the requirements of revocability, diversity, security and performance. In this context, we use the chaotic behavior of logistic map to build the projection vectors using a methodology that makes the construction of the projection matrix depend on the biometric template and its identity. The proposed approach has been evaluated and compared with Biohashing and BioPhasor using a rigorous security analysis. Our extensive experimental results using several databases (e.g., face, finger-knuckle and iris), show that the proposed technique has the ability to preserve and increase the performance of protected systems. Moreover, it is demonstrated that the security of the proposed approach is sufficiently robust to possible attacks keeping an acceptable balance between discrimination, diversity and non-invertibility.

ERGODICITY AND CHAOS IN A SYSTEM OF HARMONIC OSCILLATORS

2009 ◽  
Vol 23 (20n21) ◽  
pp. 3992-4000 ◽  
Author(s):  
M. HOWARD LEE
Keyword(s):  
Physical Theory ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Harmonic Oscillators ◽  
Physical Problems ◽  
Correct Usage ◽  
One To One ◽  
Simple Models

In recent years the term ergodicity has come into scientific vogue in various physical problems. In particular when a system exibits chaotic behavior, it is often said to be ergodic. Is it a correct usage of the term ergodicity? Does it not mean that the time and ensemble averages of a variable are equal? Are they really related one to one? We examine this issue via simple models of harmonic oscilators by means of the theorems of Birkhoff and Khinchin and also by our own physical theory of ergometry. This study also considers the chaotic behavior in the logistic map.

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