Discretization And Implicit Mapping Dynamics
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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.
Two Dimensional Quadratic Nonlinear Systems
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Author : Albert C. J. Luo
language : en
Publisher: Springer Nature
Release Date : 2022-03-29
Two Dimensional Quadratic Nonlinear Systems 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 2022-03-29 with Mathematics categories.
The book focuses on the nonlinear dynamics based on the vector fields with bivariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems based on bivariate vector fields. Such a book provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems on linear and nonlinear bivariate manifolds. Possible singular dynamics of the two-dimensional quadratic systems is discussed in detail. The dynamics of equilibriums and one-dimensional flows on bivariate manifolds are presented. Saddle-focus bifurcations are discussed, and switching bifurcations based on infinite-equilibriums are presented. Saddle-focus networks on bivariate manifolds are demonstrated. This book will serve as a reference book on dynamical systems and control for researchers, students and engineering in mathematics, mechanical and electrical engineering.
Two Dimensional Quadratic Nonlinear Systems
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Author : Albert C. J. Luo
language : en
Publisher: Springer Nature
Release Date : 2023-04-19
Two Dimensional Quadratic Nonlinear Systems 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 2023-04-19 with Mathematics categories.
This book focuses on the nonlinear dynamics based on the vector fields with univariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems. It provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems. Such a two-dimensional dynamical system is one of simplest dynamical systems in nonlinear dynamics, but the local and global structures of equilibriums and flows in such two-dimensional quadratic systems help us understand other nonlinear dynamical systems, which is also a crucial step toward solving the Hilbert’s sixteenth problem. Possible singular dynamics of the two-dimensional quadratic systems are discussed in detail. The dynamics of equilibriums and one-dimensional flows in two-dimensional systems are presented. Saddle-sink and saddle-source bifurcations are discussed, and saddle-center bifurcations are presented. The infinite-equilibrium states are switching bifurcations for nonlinear systems. From the first integral manifolds, the saddle-center networks are developed, and the networks of saddles, source, and sink are also presented. This book serves as a reference book on dynamical systems and control for researchers, students, and engineering in mathematics, mechanical, and electrical engineering.
The Many Facets Of Complexity Science
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Author : Dimitri Volchenkov
language : en
Publisher: Springer Nature
Release Date : 2021-08-30
The Many Facets Of Complexity Science written by Dimitri Volchenkov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-30 with Science categories.
This book explores recent developments in theoretical research and data analysis of real-world complex systems, organized in three parts, namely Entropy, information, and complexity functions Multistability, oscillations, and rhythmic synchronization Diffusions, rotation, and convection in fluids The collection of works devoted to the memory of Professor Valentin Afraimovich provides a deep insight into the recent developments in complexity science by introducing new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to economics, genetics, engineering vibrations, as well as classic problems in physics, fluid and climate dynamics, and urban dynamics. 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. It can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, and urban planners.
Nonlinear Dynamics Chaos And Complexity
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Author : Dimitri Volchenkov
language : en
Publisher: Springer Nature
Release Date : 2020-12-14
Nonlinear Dynamics Chaos And Complexity written by Dimitri Volchenkov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-14 with Mathematics categories.
This book demonstrates how mathematical methods and techniques can be used in synergy and create a new way of looking at complex systems. It becomes clear nowadays that the standard (graph-based) network approach, in which observable events and transportation hubs are represented by nodes and relations between them are represented by edges, fails to describe the important properties of complex systems, capture the dependence between their scales, and anticipate their future developments. Therefore, authors in this book discuss the new generalized theories capable to describe a complex nexus of dependences in multi-level complex systems and to effectively engineer their important functions. The collection of works devoted to the memory of Professor Valentin Afraimovich introduces new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to molecular biology, genetics, neurosciences, artificial intelligence as well as classic problems in physics, machine learning, brain and urban dynamics. The book can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, urban planners, and even musicians (with some mathematical background).
Memorized Discrete Systems And Time Delay
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Author : Albert C. J. Luo
language : en
Publisher: Springer
Release Date : 2016-11-18
Memorized Discrete Systems And Time Delay 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 2016-11-18 with Technology & Engineering categories.
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.
Periodic Motions To Chaos In A Spring Pendulum System
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Author : Yu Guo
language : en
Publisher: Springer Nature
Release Date : 2023-02-06
Periodic Motions To Chaos In A Spring Pendulum System written by Yu Guo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-06 with Technology & Engineering categories.
This book builds on the fundamental understandings, learned in undergraduate engineering and physics in principles of dynamics and control of mechanical systems. The design of real-world mechanical systems and devices becomes far more complex than the spring-pendulum system to which most engineers have been exposed. The authors provide one of the simplest models of nonlinear dynamical systems for learning complex nonlinear dynamical systems. The book addresses the complex challenges of the necessary modeling for the design of machines. The book addresses the methods to create a mechanical system with stable and unstable motions in environments influenced by an array of motion complexity including varied excitation frequencies ranging from periodic motions to chaos. Periodic motions to chaos, in a periodically forced nonlinear spring pendulum system, are presented through the discrete mapping method, and the corresponding stability and bifurcations of periodic motions on the bifurcation trees are presented. Developed semi-analytical solutions of periodical motions to chaos help the reader to understand complex nonlinear dynamical behaviors in nonlinear dynamical systems. Especially, one can use unstable motions rather than stable motions only.
Resonance And Bifurcation To Chaos In Pendulum
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Author : Luo Albert C J
language : en
Publisher: World Scientific
Release Date : 2017-12-15
Resonance And Bifurcation To Chaos In Pendulum written by Luo Albert C J and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-15 with Science categories.
A periodically forced mathematical pendulum is one of the typical and popular nonlinear oscillators that possess complex and rich dynamical behaviors. Although the pendulum is one of the simplest nonlinear oscillators, yet, until now, we are still not able to undertake a systematical study of periodic motions to chaos in such a simplest system due to lack of suitable mathematical methods and computational tools. To understand periodic motions and chaos in the periodically forced pendulum, the perturbation method has been adopted. One could use the Taylor series to expend the sinusoidal function to the polynomial nonlinear terms, followed by traditional perturbation methods to obtain the periodic motions of the approximated differential system. This book discusses Hamiltonian chaos and periodic motions to chaos in pendulums. This book first detects and discovers chaos in resonant layers and bifurcation trees of periodic motions to chaos in pendulum in the comprehensive fashion, which is a base to understand the behaviors of nonlinear dynamical systems, as a results of Hamiltonian chaos in the resonant layers and bifurcation trees of periodic motions to chaos. The bifurcation trees of travelable and non-travelable periodic motions to chaos will be presented through the periodically forced pendulum. Contents: Resonance and Hamiltonian ChaosHamiltonian Chaos in PendulumParametric Chaos in PendulumNonlinear Discrete SystemsPeriodic Flows in Continuous SystemsPeriodic Motions to Chaos in Pendulum Readership: Researchers and academics in the field of mathematics. Keywords: Mathematics;Resonance: Bifurcation;Chaos in Pendulum;Nonlinear Science, Chaos & Dynamical SystemsReview:0
Proceedings Of The 8th International Conference On Computational Science And Technology
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Author : Rayner Alfred
language : en
Publisher: Springer Nature
Release Date : 2022-03-25
Proceedings Of The 8th International Conference On Computational Science And Technology written by Rayner Alfred and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-25 with Technology & Engineering categories.
This book gathers the proceedings of the Seventh International Conference on Computational Science and Technology (ICCST 2021), held in Labuan, Malaysia, on 28–29 August 2021. The respective contributions offer practitioners and researchers a range of new computational techniques and solutions, identify emerging issues, and outline future research directions, while also showing them how to apply the latest large-scale, high-performance computational methods.
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.