Tackling The Inverse Problem For Non Autonomous Systems
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Tackling The Inverse Problem For Non Autonomous Systems
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Author : Tomislav Stankovski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-27
Tackling The Inverse Problem For Non Autonomous Systems written by Tomislav Stankovski 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 2013-08-27 with Science categories.
This thesis presents a new method for following evolving interactions between coupled oscillatory systems of the kind that abound in nature. Examples range from the subcellular level, to ecosystems, through climate dynamics, to the movements of planets and stars. Such systems mutually interact, adjusting their internal clocks, and may correspondingly move between synchronized and non-synchronized states. The thesis describes a way of using Bayesian inference to exploit the presence of random fluctuations, thus analyzing these processes in unprecedented detail. It first develops the basic theory of interacting oscillators whose frequencies are non-constant, and then applies it to the human heart and lungs as an example. Their coupling function can be used to follow with great precision the transitions into and out of synchronization. The method described has the potential to illuminate the ageing process as well as to improve diagnostics in cardiology, anesthesiology and neuroscience, and yields insights into a wide diversity of natural processes.
Neurodynamics
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Author : Stephen Coombes
language : en
Publisher: Springer Nature
Release Date : 2023-05-09
Neurodynamics written by Stephen Coombes and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-09 with Mathematics categories.
This book is about the dynamics of neural systems and should be suitable for those with a background in mathematics, physics, or engineering who want to see how their knowledge and skill sets can be applied in a neurobiological context. No prior knowledge of neuroscience is assumed, nor is advanced understanding of all aspects of applied mathematics! Rather, models and methods are introduced in the context of a typical neural phenomenon and a narrative developed that will allow the reader to test their understanding by tackling a set of mathematical problems at the end of each chapter. The emphasis is on mathematical- as opposed to computational-neuroscience, though stresses calculation above theorem and proof. The book presents necessary mathematical material in a digestible and compact form when required for specific topics. The book has nine chapters, progressing from the cell to the tissue, and an extensive set of references. It includes Markov chain models for ions, differential equations for single neuron models, idealised phenomenological models, phase oscillator networks, spiking networks, and integro-differential equations for large scale brain activity, with delays and stochasticity thrown in for good measure. One common methodological element that arises throughout the book is the use of techniques from nonsmooth dynamical systems to form tractable models and make explicit progress in calculating solutions for rhythmic neural behaviour, synchrony, waves, patterns, and their stability. This book was written for those with an interest in applied mathematics seeking to expand their horizons to cover the dynamics of neural systems. It is suitable for a Masters level course or for postgraduate researchers starting in the field of mathematical neuroscience.
Nonautonomous Dynamical Systems In The Life Sciences
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Author : Peter E. Kloeden
language : en
Publisher: Springer
Release Date : 2014-01-22
Nonautonomous Dynamical Systems In The Life Sciences written by Peter E. Kloeden and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-22 with Mathematics categories.
Nonautonomous dynamics describes the qualitative behavior of evolutionary differential and difference equations, whose right-hand side is explicitly time dependent. Over recent years, the theory of such systems has developed into a highly active field related to, yet recognizably distinct from that of classical autonomous dynamical systems. This development was motivated by problems of applied mathematics, in particular in the life sciences where genuinely nonautonomous systems abound. The purpose of this monograph is to indicate through selected, representative examples how often nonautonomous systems occur in the life sciences and to outline the new concepts and tools from the theory of nonautonomous dynamical systems that are now available for their investigation.
Proceedings Of The Iutam Symposium On Optimal Guidance And Control For Autonomous Systems 2023
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Author : Dilmurat Azimov
language : en
Publisher: Springer Nature
Release Date : 2024-01-05
Proceedings Of The Iutam Symposium On Optimal Guidance And Control For Autonomous Systems 2023 written by Dilmurat Azimov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-05 with Technology & Engineering categories.
This book showcases a collection of papers that present cutting-edge studies, methods, experiments, and applications in various interdisciplinary fields. These fields encompass optimal control, guidance, navigation, game theory, stability, nonlinear dynamics, robotics, sensor fusion, machine learning, and autonomy. The chapters reveal novel studies and methods, providing fresh insights into the field of optimal guidance and control for autonomous systems. The book also covers a wide range of relevant applications, showcasing how optimal guidance and control techniques can be effectively applied in various domains, including mechanical and aerospace engineering. From robotics to sensor fusion and machine learning, the papers explore the practical implications of these techniques and methodologies.
Differential Geometry Applied To Dynamical Systems With Cd Rom
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Author : Jean-marc Ginoux
language : en
Publisher: World Scientific
Release Date : 2009-04-03
Differential Geometry Applied To Dynamical Systems With Cd Rom written by Jean-marc Ginoux and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-03 with Mathematics categories.
This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory — or the flow — may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence identifying the main features of the system such as fixed points and their stability, local bifurcations of codimension one, center manifold equation, normal forms, linear invariant manifolds (straight lines, planes, hyperplanes).In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem.
Cardiorespiratory Coupling Novel Insights For Integrative Biomedicine
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Author : Tijana Bojić
language : en
Publisher: Frontiers Media SA
Release Date : 2021-06-01
Cardiorespiratory Coupling Novel Insights For Integrative Biomedicine written by Tijana Bojić and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-01 with Science categories.
Sensitivity Of Automatic Control Systems
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Author : Efim Rozenwasser
language : en
Publisher: CRC Press
Release Date : 2019-04-30
Sensitivity Of Automatic Control Systems written by Efim Rozenwasser and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-30 with Technology & Engineering categories.
Although it arose much earlier in a variety of contexts, sensitivity theory became an independent branch of science in the sixties. Since then, researchers from around the world have continued to make great strides in both the theory and its applications. However, much of the work of Russian scientific schools and specialists remain unknown in the West. Sensitivity of Control Systems summarizes the results of the authors and their disciples in sensitivity theory, addressing the basic notions of the theory and the problem of selecting technical parameters of systems. The authors formulate problems for actual technical systems and their models, and establish relations between sensitivity theory and classical stability problems. They offer a significant, general theory for investigating the sensitivity of boundary problems and use elements of this theory for sensitivity analysis of solutions to nonlinear programming and variational calculus problems, as well as oscillatory processes. The book also presents general investigation methods for discontinuous systems, including those described by operator models. Full of powerful new methods and results, this book offers a unique opportunity for those in theoretical investigation and in the design, testing, and exploitation of various control systems to explore the work of Russia's leading researchers in sensitivity theory. Furthermore, its techniques for parametric perturbation investigation, Sensitivity of Control Systems will prove useful in fields outside of control theory, including oscillation theory, motion dynamics, and mathematical economy.
Monthly Catalog Of United States Government Publications
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Author :
language : en
Publisher:
Release Date : 1994
Monthly Catalog Of United States Government Publications written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Government publications categories.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1994
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Aeronautics categories.
Handbook Of Global Analysis
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Author : Demeter Krupka
language : en
Publisher: Elsevier
Release Date : 2011-08-11
Handbook Of Global Analysis written by Demeter Krupka and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-11 with Mathematics categories.
This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents