Continuous And Discontinuous Piecewise Smooth One Dimensional Maps Invariant Sets And Bifurcation Structures
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Continuous And Discontinuous Piecewise Smooth One Dimensional Maps Invariant Sets And Bifurcation Structures
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Author : Viktor Avrutin
language : en
Publisher: World Scientific
Release Date : 2019-05-28
Continuous And Discontinuous Piecewise Smooth One Dimensional Maps Invariant Sets And Bifurcation Structures written by Viktor Avrutin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-28 with Mathematics categories.
The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.
Continuous And Discontinuous Piecewise Smooth One Dimensional Maps
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Author : Laura Gardini
language : en
Publisher:
Release Date : 2016
Continuous And Discontinuous Piecewise Smooth One Dimensional Maps written by Laura Gardini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with MATHEMATICS categories.
"Although the dynamic behavior of piecewise-smooth systems is still far from being understood completely, some significant results in this field have been achieved in the last twenty years. The investigation of these systems is important not only because they represent adequate models for many applications ranging from mechanical and electrical engineering up to financial markets, but also due to the importance of the phenomena observed in other types of dynamical systems as well. It is natural, therefore, to begin the analysis with the most simple subclass of piecewise-smooth systems (namely one-dimensional maps) for which many phenomena can be investigated much more easily than for higher-dimensional systems. In this book, we consider both continuous and discontinuous one-dimensional piecewise-linear maps and summarize the results related to bifurcation structures in regular and robust chaotic domains. The map replacement technique based on symbolic dynamics allows us to offer significantly more analytical proofs than what is usually possible"--
Advances In Discrete Dynamical Systems Difference Equations And Applications
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Author : Saber Elaydi
language : en
Publisher: Springer Nature
Release Date : 2023-03-25
Advances In Discrete Dynamical Systems Difference Equations And Applications written by Saber Elaydi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-25 with Mathematics categories.
This book comprises selected papers of the 26th International Conference on Difference Equations and Applications, ICDEA 2021, held virtually at the University of Sarajevo, Bosnia and Herzegovina, in July 2021. The book includes the latest and significant research and achievements in difference equations, discrete dynamical systems, and their applications in various scientific disciplines. The book is interesting for Ph.D. students and researchers who want to keep up to date with the latest research, developments, and achievements in difference equations, discrete dynamical systems, and their applications, the real-world problems.
New Developments In Discrete Dynamical Systems Difference Equations And Applications
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Author : Saber Elaydi
language : en
Publisher: Springer Nature
Release Date : 2025-03-25
New Developments In Discrete Dynamical Systems Difference Equations And Applications written by Saber Elaydi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-25 with Mathematics categories.
This compelling book presents remarkable contributions from esteemed speakers who participated in the 28th International Conference on Difference Equations and Applications, ICDEA 2023, hosted at Phitsanulok, Thailand, in collaboration with the International Society of Difference Equations (ISDE) from July 17 to 21, 2023. Embark on an enriching journey through the realms of difference equations and discrete dynamical systems, with practical applications spanning economics, engineering, biology, and related sciences. Immerse yourself in cutting-edge research as you explore new and significant breakthroughs within the fields of difference equations and discrete dynamical systems. This comprehensive compilation spans diverse scientific disciplines, demonstrating the profound impact of these theories and methodologies in practical and tangible settings. From economic modeling to engineering optimization, from biological systems to interdisciplinary applications, this book exemplifies the versatility and relevance of difference equations and discrete dynamical systems. Designed to resonate with a wide audience, including Ph.D. students, researchers, educators, and practitioners, it goes beyond mere dissemination of recent results. It actively fosters the advancement of knowledge, serving as a catalyst for further explorations and innovations across the spectrum of sciences.
Lozi H Non And Belykh Chaotic Attractors
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Author : René Lozi
language : en
Publisher: CRC Press
Release Date : 2024-12-30
Lozi H Non And Belykh Chaotic Attractors written by René Lozi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-30 with Mathematics categories.
Over the past fifty years, the development of chaotic dynamical systems theory and its subsequent wide applicability in science and technology has been an extremely important achievement of modern mathematics. Chaotic attractors are not a fleeting curiosity, and their continued study is important for the progress of mathematics. This book collects several of the new relevant results on the most important of them: the Lozi, Hénon and Belykh attractors. Existence proofs for strange attractors in piecewise-smooth nonlinear Lozi-Hénon and Belykh maps are given. Generalization of Lozi map in higher dimensions, Markov partition or embedding into the 2D border collision normal form of this map are considered. K-symbol fractional order discrete-time and relationship between this map and maxtype difference equations are explored. Statistical self-similarity, control of chaotic transients, and target-oriented control of Hénon and Lozi attractors are presented. Controlling chimera and solitary states by additive noise in networks of chaotic maps, detecting invariant expanding cones for generating word sets to identify chaos in piecewise-linear maps, and studying border collision bifurcations in a piecewise linear duopoly model complete this book. This book is an essential companion for students and researchers in mathematics, physics, engineering, and related disciplines seeking to deepen their understanding of chaotic dynamical systems and their applications. The chapters in this book were originally published in Journal of Difference Equations and Applications.
Nonlinear Economic Dynamics And Financial Modelling
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Author : Roberto Dieci
language : en
Publisher: Springer
Release Date : 2014-07-26
Nonlinear Economic Dynamics And Financial Modelling written by Roberto Dieci and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-26 with Business & Economics categories.
This book reflects the state of the art on nonlinear economic dynamics, financial market modelling and quantitative finance. It contains eighteen papers with topics ranging from disequilibrium macroeconomics, monetary dynamics, monopoly, financial market and limit order market models with boundedly rational heterogeneous agents to estimation, time series modelling and empirical analysis and from risk management of interest-rate products, futures price volatility and American option pricing with stochastic volatility to evaluation of risk and derivatives of electricity market. The book illustrates some of the most recent research tools in these areas and will be of interest to economists working in economic dynamics and financial market modelling, to mathematicians who are interested in applying complexity theory to economics and finance and to market practitioners and researchers in quantitative finance interested in limit order, futures and electricity market modelling, derivative pricing and risk management.
Analytical And Approximate Methods For Complex Dynamical Systems
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Author : Alexander Timokha
language : en
Publisher: Springer Nature
Release Date : 2025-03-16
Analytical And Approximate Methods For Complex Dynamical Systems written by Alexander Timokha and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-16 with Science categories.
This book presents Analytical and Approximate Methods for Complex Dynamical Systems and introduces ideas of discontinuous mapping treated as complex dynamical systems. Mathematicians of world-recognized Ukrainian scientific schools established by M.Krylov, M.Bogolyubov, Yu.Mitropolskiy, and A.Sharkovsky used to cooperate for writing the collective book whose purpose consists of illustrating a synergy of combining diverse (by idea and technique) constructive analytical and approximate approaches and methods in complex dynamical systems which are herein associated with mathematical models of networks, conflict/economic theories, sloshing, soft matter, and even levitating drops. Readers are facilitated to learn contemporary insights, fundamentals (Parts I and III), applications (Part II), and components of theories of bifurcation, synchronization/self-organization, collective dynamics, chaos, solitons, fractional differential equations, symmetry, reduced order modelling, and many others, that makes the book useful for both graduate and postgraduate students, lecturers, researchers, and even engineers dealing with multidimensional dynamic systems.
Cycles Growth And The Great Recession
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Author : Annalisa Cristini
language : en
Publisher: Routledge
Release Date : 2014-11-13
Cycles Growth And The Great Recession written by Annalisa Cristini and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-13 with Business & Economics categories.
Cycles, Growth and the Great Recession is a collection of papers that assess the nature and role of the business cycle in contemporary economies. These assessments are made in the context of the financial market instability that distinguishes the Great Recession from previous post-war slowdowns. Theorists and applied scholars in the fields of economics and mathematical economics discuss various approaches to understanding cycles and growth, and present mathematical and applied macro models to show how uncertainty shapes cycles by affecting the economic agent choice. Also included is an empirical section that investigates how the Great Recession affected households’ housing wealth, labour productivity and migration decisions. This book aims to: Propose a novel understanding of the business cycle by comparing the approaches of various scholars, starting from Hyman Minsky and Piero Ferri. Show that uncertainty is a main feature of the business cycle that affects decision-making and economic behaviour in general. Explain with mathematical models how the behaviour of economic agents can lead to cyclical paths for modern developed economies. Augment theory with empirical analysis of some central issues related to the Great Recession. This book comprises an original view of such widely discussed subjects as business cycles, uncertainty, economic growth and the Great Recession, constructed around theory, models and applications.
Frequency Domain Approach To Hopf Bifurcation Analysis Continuous Time Delayed Systems
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Author : Franco Sebastian Gentile
language : en
Publisher: World Scientific
Release Date : 2019-10-07
Frequency Domain Approach To Hopf Bifurcation Analysis Continuous Time Delayed Systems written by Franco Sebastian Gentile and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-07 with Technology & Engineering categories.
This book is devoted to the study of an effective frequency-domain approach, based on systems control theory, to compute and analyze several types of standard bifurcation conditions for general continuous-time nonlinear dynamical systems. A very rich pictorial gallery of local bifurcation diagrams for such nonlinear systems under simultaneous variations of several system parameters is presented. Some higher-order harmonic balance approximation formulas are derived for analyzing the oscillatory dynamics in small neighborhoods of certain types of Hopf and degenerate Hopf bifurcations.The frequency-domain approach is then extended to the large class of delay-differential equations, where the time delays can be either discrete or distributed. For the case of discrete delays, two alternatives are presented, depending on the structure of the underlying dynamical system, where the more general setting is then extended to the case of distributed time-delayed systems. Some representative examples in engineering and biology are discussed.
13th Chaotic Modeling And Simulation International Conference
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Author : Christos H. Skiadas
language : en
Publisher: Springer Nature
Release Date : 2021-12-14
13th Chaotic Modeling And Simulation International Conference written by Christos H. Skiadas and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-14 with Mathematics categories.
Gathering the proceedings of the 13th CHAOS2020 International Conference, this book highlights recent developments in nonlinear, dynamical and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and the Engineering Sciences. The respective chapters address key methods, empirical data and computer techniques, as well as major theoretical advances in the applied nonlinear field. Beyond showcasing the state of the art, the book will help academic and industrial researchers alike apply chaotic theory in their studies.