Discontinuity Nonlinearity And Complexity
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Discontinuity Nonlinearity And Complexity
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Author : Lev Ostrovsky
language : en
Publisher: L& H Scientific Publishing
Release Date : 2018-07-01
Discontinuity Nonlinearity And Complexity written by Lev Ostrovsky and has been published by L& H Scientific Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-01 with Mathematics categories.
The interdisciplinary journal publishes original and new results on recent developments, discoveries and progresses on Discontinuity, Nonlinearity and Complexity in physical and social sciences. The aim of the journal is to stimulate more research interest for exploration of discontinuity, complexity, nonlinearity and chaos in complex systems. The manuscripts in dynamical systems with nonlinearity and chaos are solicited, which includes mathematical theories and methods, physical principles and laws, and computational techniques. The journal provides a place to researchers for the rapid exchange of ideas and techniques in discontinuity, complexity, nonlinearity and chaos in physical and social sciences. No length limitations for contributions are set, but only concisely written manuscripts are published. Brief papers are published on the basis of Technical Notes. Discussions of previous published papers are welcome. Topics of Interest Complex and hybrid dynamical systemsDiscontinuous dynamical systems (i.e., impulsive, time-delay, flow barriers)Nonlinear discrete systems and symbolic dynamicsFractional dynamical systems and controlStochastic dynamical systems and randomnessComplexity, self-similarity and synchronization in nonlinear physicsNonlinear phenomena and physical mechanismsStability, bifurcation and chaos in complex systemsHydrodynamics, turbulence and complexity mechanismNonlinear waves and solitonDynamical networksCombinatorial aspects of dynamical systemsBiological dynamics and biophysics
Discontinuity And Complexity In Nonlinear Physical Systems
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Author : J. A. Tenreiro Machado
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-04
Discontinuity And Complexity In Nonlinear Physical Systems written by J. A. Tenreiro Machado and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-04 with Technology & Engineering categories.
Discontinuity in Nonlinear Physical Systems explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed.
Regularity And Complexity In Dynamical Systems
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Author : Albert C. J. Luo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-12
Regularity And Complexity In Dynamical Systems written by Albert C. J. Luo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-12 with Mathematics categories.
Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent years, there has been an increasing amount of interest in periodic and chaotic behaviors in discontinuous dynamical systems because such dynamical systems are prevalent in engineering. Usually, the smoothening of discontinuous dynamical system is adopted in order to use the theory of continuous dynamical systems. However, such technique cannot provide suitable results in such discontinuous systems. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.
Chaos Nonlinearity Complexity
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Author : Ashok Sengupta
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-25
Chaos Nonlinearity Complexity written by Ashok Sengupta and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-25 with Computers categories.
This book explores non-extensive statistical mechanics in non-equilibrium thermodynamics, and presents an overview of the strong nonlinearity of chaos and complexity in natural systems, drawing on relevant mathematics from topology, measure-theory, inverse and ill-posed problems, set-valued analysis, and nonlinear functional analysis. It offers a self-contained theory of complexity and complex systems as the steady state of non-equilibrium systems, denoting a homeostatic dynamic equilibrium between stabilizing order and destabilizing disorder.
Sequential Bifurcation Trees To Chaos In Nonlinear Time Delay Systems
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Author : Siyuan Xing
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Sequential Bifurcation Trees To Chaos In Nonlinear Time Delay Systems written by Siyuan Xing and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Technology & Engineering categories.
In this book, the global sequential scenario of bifurcation trees of periodic motions to chaos in nonlinear dynamical systems is presented for a better understanding of global behaviors and motion transitions for one periodic motion to another one. A 1-dimensional (1-D), time-delayed, nonlinear dynamical system is considered as an example to show how to determine the global sequential scenarios of the bifurcation trees of periodic motions to chaos. All stable and unstable periodic motions on the bifurcation trees can be determined. Especially, the unstable periodic motions on the bifurcation trees cannot be achieved from the traditional analytical methods, and such unstable periodic motions and chaos can be obtained through a specific control strategy. The sequential periodic motions in such a 1-D time-delayed system are achieved semi-analytically, and the corresponding stability and bifurcations are determined by eigenvalue analysis. Each bifurcation tree of a specific periodic motion to chaos are presented in detail. The bifurcation tree appearance and vanishing are determined by the saddle-node bifurcation, and the cascaded period-doubled periodic solutions are determined by the period-doubling bifurcation. From finite Fourier series, harmonic amplitude and harmonic phases for periodic motions on the global bifurcation tree are obtained for frequency analysis. Numerical illustrations of periodic motions are given for complex periodic motions in global bifurcation trees. The rich dynamics of the 1-D, delayed, nonlinear dynamical system is presented. Such global sequential periodic motions to chaos exist in nonlinear dynamical systems. The frequency-amplitude analysis can be used for re-construction of analytical expression of periodic motions, which can be used for motion control in dynamical systems.
Discretization And Implicit Mapping Dynamics
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Author : Albert C. J. Luo
language : en
Publisher: Springer
Release Date : 2015-07-30
Discretization And Implicit Mapping Dynamics written by Albert C. J. Luo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-30 with Science categories.
This unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed, and the explicit and implicit maps of continuous dynamical systems are developed through the single-step and multi-step discretizations. The implicit dynamics of period-m solutions in discrete nonlinear systems are discussed. The book also offers a generalized approach to finding analytical and numerical solutions of stable and unstable periodic flows to chaos in nonlinear systems with/without time-delay. The bifurcation trees of periodic motions to chaos in the Duffing oscillator are shown as a sample problem, while the discrete Fourier series of periodic motions and chaos are also presented. The book offers a valuable resource for university students, professors, researchers and engineers in the fields of applied mathematics, physics, mechanics, control systems, and engineering.
Nonlinear Dynamics And Complexity
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Author : Valentin Afraimovich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-22
Nonlinear Dynamics And Complexity written by Valentin Afraimovich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Technology & Engineering categories.
This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.
Toward Analytical Chaos In Nonlinear Systems
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Author : Albert C. J. Luo
language : en
Publisher: John Wiley & Sons
Release Date : 2014-06-23
Toward Analytical Chaos In Nonlinear Systems written by Albert C. J. Luo and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-23 with Technology & Engineering categories.
Exact analytical solutions to periodic motions in nonlinear dynamical systems are almost not possible. Since the 18th century, one has extensively used techniques such as perturbation methods to obtain approximate analytical solutions of periodic motions in nonlinear systems. However, the perturbation methods cannot provide the enough accuracy of analytical solutions of periodic motions in nonlinear dynamical systems. So the bifurcation trees of periodic motions to chaos cannot be achieved analytically. The author has developed an analytical technique that is more effective to achieve periodic motions and corresponding bifurcation trees to chaos analytically. Toward Analytical Chaos in Nonlinear Systems systematically presents a new approach to analytically determine periodic flows to chaos or quasi-periodic flows in nonlinear dynamical systems with/without time-delay. It covers the mathematical theory and includes two examples of nonlinear systems with/without time-delay in engineering and physics. From the analytical solutions, the routes from periodic motions to chaos are developed analytically rather than the incomplete numerical routes to chaos. The analytical techniques presented will provide a better understanding of regularity and complexity of periodic motions and chaos in nonlinear dynamical systems. Key features: Presents the mathematical theory of analytical solutions of periodic flows to chaos or quasieriodic flows in nonlinear dynamical systems Covers nonlinear dynamical systems and nonlinear vibration systems Presents accurate, analytical solutions of stable and unstable periodic flows for popular nonlinear systems Includes two complete sample systems Discusses time-delayed, nonlinear systems and time-delayed, nonlinear vibrational systems Includes real world examples Toward Analytical Chaos in Nonlinear Systems is a comprehensive reference for researchers and practitioners across engineering, mathematics and physics disciplines, and is also a useful source of information for graduate and senior undergraduate students in these areas.
Nonlinearity Chaos And Complexity
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Author : Cristoforo Sergio Bertuglia
language : en
Publisher: OUP Oxford
Release Date : 2005-05-12
Nonlinearity Chaos And Complexity written by Cristoforo Sergio Bertuglia and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-12 with Mathematics categories.
Covering a broad range of topics, this text provides a comprehensive survey of the modelling of chaotic dynamics and complexity in the natural and social sciences. Its attention to models in both the physical and social sciences and the detailed philosophical approach make this an unique text in the midst of many current books on chaos and complexity. Part 1 deals with the mathematical model as an instrument of investigation. The general meaning of modelling and, more specifically, questions concerning linear modelling are discussed. Part 2 deals with the theme of chaos and the origin of chaotic dynamics. Part 3 deals with the theme of complexity: a property of the systems and of their models which is intermediate between stability and chaos. Including an extensive index and bibliography along with numerous examples and simplified models, this is an ideal course text.
Nonlinear Vibration Reduction
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Author : Albert C. J. Luo
language : en
Publisher: Springer Nature
Release Date : 2022-11-30
Nonlinear Vibration Reduction written by Albert C. J. Luo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-30 with Technology & Engineering categories.
The tuned mass damper is one of the classic dynamic vibration absorbers with effective devices for energy dissipation and vibration reduction. The electromagnetically tuned mass damper system is extensively used for vibration reduction in engineering. A better understanding of the nonlinear dynamics of the electromagnetically tuned mass damper system is very important to optimize the parameters of such systems for vibration reduction. However, until now, one cannot fully understand complex periodic motions in such a nonlinear, electromagnetically tuned mass damper system. In this book, the semi-analytical solutions of periodic motions are presented through period-1, period-3, period-9, and period-12 motions. The corresponding stability and bifurcations of periodic motions are determined. The frequency-amplitude characteristics for bifurcation routes of such higher-order periodic motions are presented. This book helps people better understand the dynamical behaviors of an electromagnetically tuned mass damper system for the new development and design of vibration reduction and energy harvesting systems.