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Books > Business & Economics > Economics > Econometrics > General

A Primer for Unit Root Testing (Hardcover): K. Patterson A Primer for Unit Root Testing (Hardcover)
K. Patterson
R2,663 Discovery Miles 26 630 Ships in 18 - 22 working days

This book provides an introduction to the technical background of unit root testing, one of the most heavily researched areas in econometrics over the last twenty years. Starting from an elementary understanding of probability and time series, it develops the key concepts necessary to understand the structure of random walks and brownian motion, and their role in tests for a unit root. The techniques are illustrated with worked examples, data and programs available on the book's website, which includes more numerical and theoretical examples
This book is indispensable reading for all interested in Time Series Econometrics, Econometrics and Applied Econometrics

Economic Growth and Environmental Quality in a Post-Pandemic World - New Directions in the Econometrics of the Environmental... Economic Growth and Environmental Quality in a Post-Pandemic World - New Directions in the Econometrics of the Environmental Kuznets Curve (Hardcover)
Muhammad Shahbaz, Daniel Balsalobre-Lorente, Rajesh Sharma
R4,512 Discovery Miles 45 120 Ships in 10 - 15 working days

In response to the damage caused by a growth-led global economy, researchers across the world started investigating the association between environmental pollution and its possible determinants using different models and techniques. Most famously, the environmental Kuznets curve hypothesizes an inverted U-shaped association between environmental quality and gross domestic product (GDP). This book explores the latest literature on the environmental Kuznets curve, including developments in the methodology, the impacts of the pandemic, and other recent findings. Researchers have recently broadened the range of the list of drivers of environmental pollution under consideration, which now includes variables such as foreign direct investment, trade expansion, financial development, human activities, population growth, and renewable and nonrenewable energy resources, all of which vary across different countries and times. And in addition to CO2 emissions, other proxies for environmental quality – such as water, land, and ecological footprints – have been used in recent studies. This book also incorporates analysis of the relationship between economic growth and the environment during the COVID-19 crisis, presenting new empirical work on the impact of the pandemic on energy use, the financial sector, trade, and tourism. Collectively, these developments have improved the direction and extent of the environmental Kuznets curve hypothesis and broadened the basket of dependent and independent variables which may be incorporated. This book will be invaluable reading for researchers in environmental economics and econometrics.

Global Economic Uncertainties and Exchange Rate Shocks - Transmission Channels to the South African Economy (Hardcover, 1st ed.... Global Economic Uncertainties and Exchange Rate Shocks - Transmission Channels to the South African Economy (Hardcover, 1st ed. 2017)
Eliphas Ndou, Nombulelo Gumata, Mthuli Ncube
R2,718 Discovery Miles 27 180 Ships in 18 - 22 working days

This book examines the macroeconomic and regulatory impact of domestic and international shocks on the South African economy resulting from the 2009 financial crisis. It also assesses the impact of the US economy's eventual recovery from the crisis and the prospect of higher US interest rates in future. Told in three parts, the book explores associations between economic growth, policy uncertainty and the key domestic and international transmission channels, and transmission effects, of global financial regulatory and domestic macro-economic uncertainties on subdued and volatile economic recovery, financial channels, lending rate margins, and credit growth. The book concludes by extending its focus to the role of US monetary policy, capital flows and rand/US dollar volatility on the South African economy.

Recent Econometric Techniques for Macroeconomic and Financial Data (Hardcover, 1st ed. 2021): Gilles Dufrenot, Takashi Matsuki Recent Econometric Techniques for Macroeconomic and Financial Data (Hardcover, 1st ed. 2021)
Gilles Dufrenot, Takashi Matsuki
R4,007 Discovery Miles 40 070 Ships in 10 - 15 working days

The book provides a comprehensive overview of the latest econometric methods for studying the dynamics of macroeconomic and financial time series. It examines alternative methodological approaches and concepts, including quantile spectra and co-spectra, and explores topics such as non-linear and non-stationary behavior, stochastic volatility models, and the econometrics of commodity markets and globalization. Furthermore, it demonstrates the application of recent techniques in various fields: in the frequency domain, in the analysis of persistent dynamics, in the estimation of state space models and new classes of volatility models. The book is divided into two parts: The first part applies econometrics to the field of macroeconomics, discussing trend/cycle decomposition, growth analysis, monetary policy and international trade. The second part applies econometrics to a wide range of topics in financial economics, including price dynamics in equity, commodity and foreign exchange markets and portfolio analysis. The book is essential reading for scholars, students, and practitioners in government and financial institutions interested in applying recent econometric time series methods to financial and economic data.

Mathematical Foundations of Time Series Analysis - A Concise Introduction (Hardcover, 1st ed. 2017): Jan Beran Mathematical Foundations of Time Series Analysis - A Concise Introduction (Hardcover, 1st ed. 2017)
Jan Beran
R3,998 Discovery Miles 39 980 Ships in 10 - 15 working days

This book provides a concise introduction to the mathematical foundations of time series analysis, with an emphasis on mathematical clarity. The text is reduced to the essential logical core, mostly using the symbolic language of mathematics, thus enabling readers to very quickly grasp the essential reasoning behind time series analysis. It appeals to anybody wanting to understand time series in a precise, mathematical manner. It is suitable for graduate courses in time series analysis but is equally useful as a reference work for students and researchers alike.

Applied Econometrics (Paperback, 4th edition): Dimitrios Asteriou, Stephen G. Hall Applied Econometrics (Paperback, 4th edition)
Dimitrios Asteriou, Stephen G. Hall
R831 Discovery Miles 8 310 Ships with 15 working days

This trusted textbook returns in its 4th edition with even more exercises to help consolidate understanding - and a companion website featuring additional materials, including a solutions manual for instructors. Offering a unique blend of theory and practical application, it provides ideal preparation for doing applied econometric work as it takes students from a basic level up to an advanced understanding in an intuitive, step-by-step fashion. Clear presentation of economic tests and methods of estimation is paired with practical guidance on using several types of software packages. Using real world data throughout, the authors place emphasis upon the interpretation of results, and the conclusions to be drawn from them in econometric work. This book will be essential reading for economics undergraduate and master's students taking a course in applied econometrics. Its practical nature makes it ideal for modules requiring a research project. New to this Edition: - Additional practical exercises throughout to help consolidate understanding - A freshly-updated companion website featuring a new solutions manual for instructors

Productivity and Inequality (Hardcover, 1st ed. 2018): William H. Greene, Lynda Khalaf, Paul Makdissi, Robin C. Sickles,... Productivity and Inequality (Hardcover, 1st ed. 2018)
William H. Greene, Lynda Khalaf, Paul Makdissi, Robin C. Sickles, Michael Veall, …
R4,305 Discovery Miles 43 050 Ships in 18 - 22 working days

The volume highlights the state-of-the-art knowledge (including data analysis) of productivity, inequality and efficiency analysis. It showcases a selection of the best papers from the 9th North American Productivity Workshop. These papers are relevant to academia, but also to public and private sectors in terms of the challenges that firms, financial institutions, governments, and individuals may face when dealing with economic and education related activities that lead to increase or decrease of productivity. The volume also aims to bring together ideas from different parts of the world about the challenges those local economies and institutions may face when changes in productivity are observed. These contributions focus on theoretical and empirical research in areas including productivity, production theory and efficiency measurement in economics, management science, operation research, public administration, and education. The North American Productivity Workshop (NAPW) brings together academic scholars and practitioners in the field of productivity and efficiency analysis from all over the world, and this proceedings volume is a reflection of this mission. The papers in this volume also address general topics as education, health, energy, finance, agriculture, transport, utilities, and economic development, among others. The editors are comprised of the 2016 local organizers, program committee members, and celebrated guest conference speakers.

The Socialist Industrial State - Towards a Political Sociology of State Socialism (Hardcover): David Lane The Socialist Industrial State - Towards a Political Sociology of State Socialism (Hardcover)
David Lane
R3,072 Discovery Miles 30 720 Ships in 10 - 15 working days

The Socialist Industrial State (1976) examines the state-socialist system, taking as the central example the Soviet Union - where the goals and values of Marxism-Leninism and the particular institutions, the form of economy and polity, were first adopted and developed. It then considers the historical developments, differences in culture, the level of economic development and the political processes of different state-socialist countries around the globe.

Discrete Models of Financial Markets (Hardcover, New): Marek Capin'ski, Ekkehard Kopp Discrete Models of Financial Markets (Hardcover, New)
Marek Capin'ski, Ekkehard Kopp
R1,572 R1,409 Discovery Miles 14 090 Save R163 (10%) Ships in 10 - 15 working days

This book explains in simple settings the fundamental ideas of financial market modelling and derivative pricing, using the no-arbitrage principle. Relatively elementary mathematics leads to powerful notions and techniques - such as viability, completeness, self-financing and replicating strategies, arbitrage and equivalent martingale measures - which are directly applicable in practice. The general methods are applied in detail to pricing and hedging European and American options within the Cox-Ross-Rubinstein (CRR) binomial tree model. A simple approach to discrete interest rate models is included, which, though elementary, has some novel features. All proofs are written in a user-friendly manner, with each step carefully explained and following a natural flow of thought. In this way the student learns how to tackle new problems.

Monetary Policy in Rwanda - 1964-Present (Hardcover, 1st ed. 2021): Thomas Kigabo Rusuhuzwa Monetary Policy in Rwanda - 1964-Present (Hardcover, 1st ed. 2021)
Thomas Kigabo Rusuhuzwa
R2,653 Discovery Miles 26 530 Ships in 18 - 22 working days

This book analyzes evolution of monetary policy in Rwanda since it was first implemented by the National Bank of Rwanda in 1964 when the bank was established. It contributes to the understanding of monetary policy which is formulation and implementation in different stages of development of a financial system that comprises the financial market (money market and capital market), financial intermediaries such as commercial banks, and the financial sector infrastructures such as payment systems and the credit reference bureau. The book breaks down applied empirical research on the assessment of key assumptions of a monetary targeting framework, namely the stability of money multiplier and money demand using econometrics of time series, through a number of case studies. Presenting a detailed empirical analysis of the monetary transmission mechanism, one of the most analyzed topics in central banks in advanced economies, this book is a valuable read for central bankers and other researchers of monetary policy, particularly in developing economies.

Essays in Honour of Fabio Canova (Hardcover): Juan J. Dolado, Luca Gambetti, Christian Matthes Essays in Honour of Fabio Canova (Hardcover)
Juan J. Dolado, Luca Gambetti, Christian Matthes
R2,978 Discovery Miles 29 780 Ships in 10 - 15 working days

Both parts of Volume 44 of Advances in Econometrics pay tribute to Fabio Canova for his major contributions to economics over the last four decades. Throughout his long and distinguished career, Canova's research has achieved both a prolific publication record and provided stellar research to the profession. His colleagues, co-authors and PhD students wish to express their deep gratitude to Fabio for his intellectual leadership and guidance, whilst showcasing the extensive advances in knowledge and theory made available by Canova for professionals in the field. Advances in Econometrics publishes original scholarly econometrics papers with the intention of expanding the use of developed and emerging econometric techniques by disseminating ideas on the theory and practice of econometrics throughout the empirical economic, business and social science literature. Annual volume themes, selected by the Series Editors, are their interpretation of important new methods and techniques emerging in economics, statistics and the social sciences.

An Economic Interpretation of Linear Programming (Hardcover, 1st ed. 2015): Quirino Paris An Economic Interpretation of Linear Programming (Hardcover, 1st ed. 2015)
Quirino Paris
R3,591 Discovery Miles 35 910 Ships in 10 - 15 working days

This text covers the basic theory and computation for mathematical modeling in linear programming. It provides a strong background on how to set up mathematical proofs and high-level computation methods, and includes substantial background material and direction. Paris presents an intuitive and novel discussion of what it means to solve a system of equations that is a crucial stepping stone for solving any linear program. The discussion of the simplex method for solving linear programs gives an economic interpretation to every step of the simplex algorithm. The text combines in a unique and novel way the microeconomics of production with the structure of linear programming to give students and scholars of economics a clear notion of what it means, formulating a model of economic equilibrium and the computation of opportunity cost in the presence of many outputs and inputs.

Applications of Differential Geometry to Econometrics (Paperback): Paul Marriott, Mark Salmon Applications of Differential Geometry to Econometrics (Paperback)
Paul Marriott, Mark Salmon
R1,197 Discovery Miles 11 970 Ships in 10 - 15 working days

Although geometry has always aided intuition in econometrics, more recently differential geometry has become a standard tool in the analysis of statistical models, offering a deeper appreciation of existing methodologies and highlighting the essential issues which can be hidden in an algebraic development of a problem. Originally published in 2000, this volume was an early example of the application of these techniques to econometrics. An introductory chapter provides a brief tutorial for those unfamiliar with the tools of Differential Geometry. The topics covered in the following chapters demonstrate the power of the geometric method to provide practical solutions and insight into problems of econometric inference.

Online and Matching-Based Market Design (Hardcover): Federico Echenique, Nicole Immorlica, Vijay V. Vazirani Online and Matching-Based Market Design (Hardcover)
Federico Echenique, Nicole Immorlica, Vijay V. Vazirani; Foreword by Alvin E. Roth
R1,962 R1,696 Discovery Miles 16 960 Save R266 (14%) Ships in 10 - 15 working days

The rich, multi-faceted and multi-disciplinary field of matching-based market design is an active and important one due to its highly successful applications with economic and sociological impact. Its home is economics, but with intimate connections to algorithm design and operations research. With chapters contributed by over fifty top researchers from all three disciplines, this volume is unique in its breadth and depth, while still being a cohesive and unified picture of the field, suitable for the uninitiated as well as the expert. It explains the dominant ideas from computer science and economics underlying the most important results on market design and introduces the main algorithmic questions and combinatorial structures. Methodologies and applications from both the pre-Internet and post-Internet eras are covered in detail. Key chapters discuss the basic notions of efficiency, fairness and incentives, and the way market design seeks solutions guided by normative criteria borrowed from social choice theory.

Inflation Dynamic - Global Positive Economic Analysis (Hardcover): Weshah Razzak Inflation Dynamic - Global Positive Economic Analysis (Hardcover)
Weshah Razzak
R4,210 Discovery Miles 42 100 Ships in 10 - 15 working days

This book explains inflation dynamic, using time series data from 1960 for 42 countries. These countries are different in every aspect, historically, culturally, socially, politically, institutionally, and economically. They are chosen on the basis of the data availability only and cover the Middle East and North Africa (MENA) region, Africa, Asia, the Caribbean, Europe, Australasia, and the United States. Inflation reached double digits in the developed countries in the 1970s and 80s, and then central banks, successfully stabilized it by anchoring inflation expectations for decades, until now. Conditional on common and country-specific shocks such as oil price shocks, financial and banking and political crises, wars, pandemics, natural disasters etc., the book tests various theoretical models about the long and short run relationships between money and prices, money growth and inflation, money growth and real output, expected inflation; the output gap, fiscal policy, and inflation, using a number of parametric and non-parametric methods, and pays attention to specifications and estimations problems. In addition, it explains why policymakers in inflation - targeting countries, e.g. the U.S., failed to anticipate the recent sudden rise in inflation. And, it examines the fallibility of the Modern Monetary Theory's policy prescription to reduce inflation by raising taxes. This is a unique and innovative book, which will find an audience among students, academics, researchers, policy makers, analysts in corporations, private and central banks and international monetary institutions.

Methodology & Tacit Knowledge - Two Experiments in  Econometrics (Hardcover): J.R. Magnus Methodology & Tacit Knowledge - Two Experiments in Econometrics (Hardcover)
J.R. Magnus
R2,824 Discovery Miles 28 240 Ships in 10 - 15 working days

"Econometrics textbooks see their subject as a set of techniques; Magnus and Morgan see it as a set of practices. A combination of controlled experiment and anthropology of science, Methodology and Tacit Knowledge gives a rare inside view of how econometricians work, why econometrics is an art and not a set of simple recipes, and why, like all artists, econometricians differ in their techniques and finished works. This is economic methodology at its best." Kevin Hoover, University of California, Davis

"The tacit knowledge experiment was a highly commendable initiative. Its exploration of the theme of how knowledge is acquired and used in applied econometrics is unique and produced some fascinating insights into this process." Adrian Pagan, Australian National University

"It is rare, perhaps unique, to find leading empirical economists face the prospect of modelling the same phenomena, with the same data within the same limited time frame. A valuable and illuminating experiment in comparative research methodologies, made all the more provocative when compared to the excellent original study by Tobin." Richard Blundell, University College London

This book will be of considerable interest to economists and to econometricians concerned about the methodology of their own discipline, and will provide valuable material for researchers in science studies and for teachers of econometrics.

Advances in Cross-Section Data Methods in Applied Economic Research - 2019 International Conference on Applied Economics (ICOAE... Advances in Cross-Section Data Methods in Applied Economic Research - 2019 International Conference on Applied Economics (ICOAE 2019) (Hardcover, 1st ed. 2020)
Nicholas Tsounis, Aspasia Vlachvei
R4,161 Discovery Miles 41 610 Ships in 18 - 22 working days

This proceedings volume presents new methods and applications in applied economics with special interest in advanced cross-section data estimation methodology. Featuring select contributions from the 2019 International Conference on Applied Economics (ICOAE 2019) held in Milan, Italy, this book explores areas such as applied macroeconomics, applied microeconomics, applied financial economics, applied international economics, applied agricultural economics, applied marketing and applied managerial economics. International Conference on Applied Economics (ICOAE) is an annual conference that started in 2008, designed to bring together economists from different fields of applied economic research, in order to share methods and ideas. Applied economics is a rapidly growing field of economics that combines economic theory with econometrics, to analyze economic problems of the real world, usually with economic policy interest. In addition, there is growing interest in the field of applied economics for cross-section data estimation methods, tests and techniques. This volume makes a contribution in the field of applied economic research by presenting the most current research. Featuring country specific studies, this book is of interest to academics, students, researchers, practitioners, and policy makers in applied economics, econometrics and economic policy.

Fuzzy Decision-Making Methods Based on Prospect Theory and Its Application in Venture Capital (Hardcover, 1st ed. 2021): Xiaoli... Fuzzy Decision-Making Methods Based on Prospect Theory and Its Application in Venture Capital (Hardcover, 1st ed. 2021)
Xiaoli Tian, Zeshui Xu
R3,332 Discovery Miles 33 320 Ships in 18 - 22 working days

This book gives a thorough and systematic introduction to the latest research results about fuzzy decision-making method based on prospect theory. It includes eight chapters: Introduction, Intuitionistic fuzzy MADM based on prospect theory, QUALIFLEX based on prospect theory with probabilistic linguistic information, Group PROMETHEE based on prospect theory with hesitant fuzzy linguistic information, Prospect consensus with probabilistic hesitant fuzzy preference information, Improved TODIM based on prospect theory and the improved TODIM with probabilistic hesitant fuzzy information, etc. This book is suitable for the researchers in the fields of fuzzy mathematics, operations research, behavioral science, management science and engineering, etc. It is also useful as a textbook for postgraduate and senior-year undergraduate students of the relevant professional institutions of higher learning.

China's Provincial Economic Competitiveness and Policy Outlook for the 13th Five-year Plan Period (2016-2020) (Hardcover,... China's Provincial Economic Competitiveness and Policy Outlook for the 13th Five-year Plan Period (2016-2020) (Hardcover, 1st ed. 2018)
Jian-Ping Li, Minrong Li, Yanjing Gao, Jianjian Li, Hongwen Su, …
R1,427 Discovery Miles 14 270 Ships in 18 - 22 working days

This book focuses on the competitive situation and policy outlook of China's provincial economy in the 13th five-year period. It begins with a general evaluation report on the country's provincial comprehensive Economic Competitiveness, followed by analyses at the international, national and regional levels, industrial and enterprise levels. On the basis of domestic and international research findings, it further enriches our understanding of provincial competitiveness, analyzes the domestic and international situation, explores new changes, new norms, new situations and new challenges concerning China's provincial economy in the past few years, reveals the characteristics and relative differences of different types, defines their internal competitive strengths and weaknesses, and provides valuable theoretical content to guide decision-making.

Global Analysis of Dynamic Models in Economics and Finance - Essays in Honour of Laura Gardini (Hardcover, 2013 ed.):... Global Analysis of Dynamic Models in Economics and Finance - Essays in Honour of Laura Gardini (Hardcover, 2013 ed.)
Gian-Italo Bischi, Carl Chiarella, Iryna Sushko
R2,725 Discovery Miles 27 250 Ships in 18 - 22 working days

The essays in this special volume survey some of the most recent advances in the global analysis of dynamic models for economics, finance and the social sciences. They deal in particular with a range of topics from mathematical methods as well as numerous applications including recent developments on asset pricing, heterogeneous beliefs, global bifurcations in complementarity games, international subsidy games and issues in economic geography. A number of stochastic dynamic models are also analysed. The book is a collection of essays in honour of the 60th birthday of Laura Gardini.

Economic Foundations of Symmetric Programming (Hardcover): Quirino Paris Economic Foundations of Symmetric Programming (Hardcover)
Quirino Paris
R2,603 Discovery Miles 26 030 Ships in 10 - 15 working days

The search for symmetry is part of the fundamental scientific paradigm in mathematics and physics. Can this be valid also for economics? This book represents an attempt to explore this possibility. The behavior of price-taking producers, monopolists, monopsonists, sectoral market equilibria, behavior under risk and uncertainty, and two-person zero- and non-zero-sum games are analyzed and discussed under the unifying structure called the linear complementarity problem. Furthermore, the equilibrium problem allows for the relaxation of often-stated but unnecessary assumptions. This unifying approach offers the advantage of a better understanding of the structure of economic models. It also introduces the simplest and most elegant algorithm for solving a wide class of problems.

An Introduction to Economic Dynamics - Modelling, Analysis and Simulation (Paperback): Srinivas Raghavendra, Petri T. Piiroinen An Introduction to Economic Dynamics - Modelling, Analysis and Simulation (Paperback)
Srinivas Raghavendra, Petri T. Piiroinen
R1,554 Discovery Miles 15 540 Ships in 10 - 15 working days

• Introduces the dynamics, principles and mathematics behind ten macroeconomic models allowing students to visualise the models and understand the economic intuition behind them. • Provides a step-by-step guide, and the necessary MATLAB codes, to allow readers to simulate and experiment with the models themselves.

Commodity Supply Management by Producing Countries - A Case-Study of the Tropical Beverage Crops (Hardcover): Alfred Maizels,... Commodity Supply Management by Producing Countries - A Case-Study of the Tropical Beverage Crops (Hardcover)
Alfred Maizels, Robert Bacon, George Mavrotas
R1,856 Discovery Miles 18 560 Ships in 10 - 15 working days

The collapse in commodity prices since 1980 has been a major cause of the economic crisis in a large number of developing countries. This book investigates whether the commodity-producing countries, by joint action, could have prevented the price collapse by appropriate supply management. The analysis is focused on the markets for the tropical beverage crops: coffee, cocoa, and tea. Using new econometric models for each market, the impact of alternative supply management schemes on supply, consumption, prices, and export earnings is simulated for the later 1980s. The results indicate that supply management by producing countries would, indeed, have been a viable alternative to the `free market' approach favoured by the developed countries. This has important implications for current international commodity policy, and, in particular, for future joint action by producing countries to overcome persistent commodity surpluses as a complement to needed diversification.

Handbook of Field Experiments, Volume 2 (Hardcover): Esther Duflo, Abhijit Banerjee Handbook of Field Experiments, Volume 2 (Hardcover)
Esther Duflo, Abhijit Banerjee
R3,521 Discovery Miles 35 210 Ships in 10 - 15 working days

Handbook of Field Experiments, Volume Two explains how to conduct experimental research, presents a catalog of research to date, and describes which areas remain to be explored. The new volume includes sections on field experiments in education in developing countries, how to design social protection programs, a section on how to combat poverty, and updates on data relating to the impact and determinants of health levels in low-income countries. Separating itself from circumscribed debates of specialists, this volume surpasses the many journal articles and narrowly-defined books written by practitioners. This ongoing series will be of particular interest to scholars working with experimental methods. Users will find results from politics, education, and more.

Memorized Discrete Systems and Time-delay (Hardcover, 1st ed. 2017): Albert C.J. Luo Memorized Discrete Systems and Time-delay (Hardcover, 1st ed. 2017)
Albert C.J. Luo
R3,941 R3,410 Discovery Miles 34 100 Save R531 (13%) Ships in 10 - 15 working days

This book examines discrete dynamical systems with memory-nonlinear systems that exist extensively in biological organisms and financial and economic organizations, and time-delay systems that can be discretized into the memorized, discrete dynamical systems. It book further discusses stability and bifurcations of time-delay dynamical systems that can be investigated through memorized dynamical systems as well as bifurcations of memorized nonlinear dynamical systems, discretization methods of time-delay systems, and periodic motions to chaos in nonlinear time-delay systems. The book helps readers find analytical solutions of MDS, change traditional perturbation analysis in time-delay systems, detect motion complexity and singularity in MDS; and determine stability, bifurcation, and chaos in any time-delay system.

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