On Complex Artificial Higher Order Neural Networks: Dealing with Stochasticity, Jumps and Delays

On Complex Artificial Higher Order Neural Networks: Dealing with Stochasticity, Jumps and Delays

Zidong Wang (Brunel University, UK), Yurong Liu (Yangzhou University, China) and Xiaohui Liu (Brunel University, UK)
Copyright: © 2009 |Pages: 378
DOI: 10.4018/978-1-59904-897-0.ch021
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Abstract

This chapter deals with the analysis problem of the global exponential stability for a general class of stochastic artificial higher order neural networks with multiple mixed time delays and Markovian jumping parameters. The mixed time delays under consideration comprise both the discrete time-varying delays and the distributed time-delays. The main purpose of this chapter is to establish easily verifiable conditions under which the delayed high-order stochastic jumping neural network is exponentially stable in the mean square in the presence of both the mixed time delays and Markovian switching. By employing a new Lyapunov-Krasovskii functional and conducting stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the criteria ensuring the exponential stability. Furthermore, the criteria are dependent on both the discrete time-delay and distributed time-delay, hence less conservative. The proposed criteria can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria.

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Dedication
Table of Contents
Acknowledgment
Ming Zhang
Chapter 1
Ming Zhang
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Artificial Higher Order Neural Network Nonlinear Models: SAS NLIN or HONNs?
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Chapter 2
Adam Knowles, Abir Hussain, Wael El Deredy, Paulo G.J. Lisboa, Christian L. Dunis
Multi-Layer Perceptrons (MLP) are the most common type of neural network in use, and their ability to perform complex nonlinear mappings and... Sample PDF
Higher Order Neural Networks with Bayesian Confidence Measure for the Prediction of the EUR/USD Exchange Rate
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Chapter 3
Da Shi, Shaohua Tan, Shuzhi Sam Ge
Real-world financial systems are often nonlinear, do not follow any regular probability distribution, and comprise a large amount of financial... Sample PDF
Automatically Identifying Predictor Variables for Stock Return Prediction
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Chapter 4
John Seiffertt, Donald C. Wunsch II
As the study of agent-based computational economics and finance grows, so does the need for appropriate techniques for the modeling of complex... Sample PDF
Higher Order Neural Network Architectures for Agent-Based Computational Economics and Finance
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Chapter 5
Yuehui Chen, Peng Wu, Qiang Wu
Forecasting exchange rates is an important financial problem that is receiving increasing attention especially because of its difficulty and... Sample PDF
Foreign Exchange Rate Forecasting Using Higher Order Flexible Neural Tree
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Chapter 6
Yuehui Chen, Peng Wu, Qiang Wu
Artificial Neural Networks (ANNs) have become very important in making stock market predictions. Much research on the applications of ANNs has... Sample PDF
Higher Order Neural Networks for Stock Index Modeling
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Chapter 7
Ming Zhang
This chapter develops a new nonlinear model, Ultra high frequency Trigonometric Higher Order Neural Networks (UTHONN), for time series data... Sample PDF
Ultra High Frequency Trigonometric Higher Order Neural Networks for Time Series Data Analysis
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Chapter 8
Panos Liatsis, Abir Hussain, Efstathios Milonidis
The research described in this chapter is concerned with the development of a novel artificial higher order neural networks architecture called the... Sample PDF
Artificial Higher Order Pipeline Recurrent Neural Networks for Financial Time Series Prediction
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Chapter 9
Abir Hussain, Panos Liatsis
The research described in this chapter is concerned with the development of a novel artificial higherorder neural networks architecture called the... Sample PDF
A Novel Recurrent Polynomial Neural Network for Financial Time Series Prediction
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Chapter 10
David R. Selviah, Janti Shawash
Generalized correlation higher order neural network designs are developed. Their performance is compared with that of first order networks... Sample PDF
Generalized Correlation Higher Order Neural Networks for Financial Time Series Prediction
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Chapter 11
Godfrey C. Onwubolu
Real world problems are described by nonlinear and chaotic processes, which makes them hard to model and predict. This chapter first compares the... Sample PDF
Artificial Higher Order Neural Networks in Time Series Prediction
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Chapter 12
Rozaida Ghazali, Dhiya Al-Jumeily
This chapter discusses the use of two artificial Higher Order Neural Networks (HONNs) models; the Pi- Sigma Neural Networks and the Ridge Polynomial... Sample PDF
Application of Pi-Sigma Neural Networks and Ridge Polynomial Neural Networks to Financial Time Series Prediction
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Chapter 13
Edgar N. Sanchez, Alma Y. Alanis, Jesús Rico
In this chapter, we propose the use of Higher Order Neural Networks (HONNs) trained with an extended Kalman filter based algorithm to predict the... Sample PDF
Electric Load Demand and Electricity Prices ForecastingUsing Higher Order Neural Networks Trained by Kalman Filtering
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Chapter 14
Shuxiang Xu
Business is a diversified field with general areas of specialisation such as accounting, taxation, stock market, and other financial analysis.... Sample PDF
Adaptive Higher Order Neural Network Models and Their Applications in Business
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Chapter 15
Jean X. Zhang
This chapter proposes nonlinear models using artificial neural network models to study the relationship between chief elected official (CEO) tenure... Sample PDF
CEO Tenure and Debt: An Artificial Higher Order Neural Network Approach
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Chapter 16
Christian L. Dunis, Jason Laws, Ben Evans
This chapter investigates the soybean-oil “crush” spread, that is the profit margin gained by processing soybeans into soyoil. Soybeans form a large... Sample PDF
Modelling and Trading the Soybean-Oil Crush Spread with Recurrent and Higher Order Networks: A Comparative Analysis
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Chapter 17
Madan M. Gupta, Noriyasu Homma, Zeng-Guang Hou, Ashu M. G. Solo, Takakuni Goto
In this chapter, we aim to describe fundamental principles of artificial higher order neural units (AHONUs) and networks (AHONNs). An essential core... Sample PDF
Fundamental Theory of Artificial Higher Order Neural Networks
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Chapter 18
Jinde Cao, Fengli Ren, Jinling Liang
This chapter concentrates on studying the dynamics of artificial higher order neural networks (HONNs) with delays. Both stability analysis and... Sample PDF
Dynamics in Artificial Higher Order Neural Networks with Delays
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Chapter 19
Zhao Lu, Leang-san Shieh, Guanrong Chen
Aiming to develop a systematic approach for optimizing the structure of artificial higher order neural networks (HONN) for system modeling and... Sample PDF
A New Topology for Artificial Higher Order Neural Networks: Polynomial Kernel Networks
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Chapter 20
David R. Selviah
This chapter describes the progress in using optical technology to construct high-speed artificial higher order neural network systems. The chapter... Sample PDF
High Speed Optical Higher Order Neural Networks for Discovering Data Trends and Patterns in Very Large Databases
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Chapter 21
Zidong Wang, Yurong Liu, Xiaohui Liu
This chapter deals with the analysis problem of the global exponential stability for a general class of stochastic artificial higher order neural... Sample PDF
On Complex Artificial Higher Order Neural Networks: Dealing with Stochasticity, Jumps and Delays
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Chapter 22
Lei Zhang, Simeon J. Simoff, Jing Chun Zhang
This chapter introduces trigonometric polynomial higher order neural network models. In the area of financial data simulation and prediction, there... Sample PDF
Trigonometric Polynomial Higher Order Neural Network Group Models and Weighted Kernel Models for Financial Data Simulation and Prediction
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