Weak Noise Induced Phenomena In A Slow Fast Dynamical System

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Noise Induced Phenomena In Slow Fast Dynamical Systems

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Author : Nils Berglund
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-07

Noise Induced Phenomena In Slow Fast Dynamical Systems written by Nils Berglund 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 2006-02-07 with Mathematics categories.

Stochastic differential equations play an increasingly important role in modeling the dynamics of a large variety of systems in the natural sciences, and in technological applications. This book is aimed at advanced undergraduate and graduate students, and researchers in mathematics, physics, the natural sciences, and engineering. It presents a new constructive approach to the quantitative description of solutions to systems of stochastic differential equations evolving on well-separated timescales. The method, which combines techniques from stochastic analysis and singular perturbation theory, allows the domains of concentration for typical sample paths to be determined, and provides precise estimates on the transition probabilities between these domains. In addition to the detailed presentation of the set-up and mathematical results, applications to problems in physics, biology, and climatology are discussed.

Weak Noise Induced Phenomena In A Slow Fast Dynamical System

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Author : Marius Emar Yamakou
language : en
Publisher:
Release Date : 2018

Weak Noise Induced Phenomena In A Slow Fast Dynamical System written by Marius Emar Yamakou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.

Noise Induced Phenomena In The Environmental Sciences

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Author : Luca Ridolfi
language : en
Publisher: Cambridge University Press
Release Date : 2011-06-20

Noise Induced Phenomena In The Environmental Sciences written by Luca Ridolfi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-20 with Science categories.

Randomness is ubiquitous in nature. Random drivers are generally considered a source of disorder in environmental systems. However, the interaction between noise and nonlinear dynamics may lead to the emergence of a number of ordered behaviors (in time and space) that would not exist in the absence of noise. This counterintuitive effect of randomness may play a crucial role in environmental processes. For example, seemingly 'random' background events in the atmosphere can grow into larger instabilities that have great effects on weather patterns. This book presents the basics of the theory of stochastic calculus and its application to the study of noise-induced phenomena in environmental systems. It will be an invaluable reference text for ecologists, geoscientists and environmental engineers interested in the study of stochastic environmental dynamics.

Stochastic Resonance

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Author : Samuel Herrmann
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-12-11

Stochastic Resonance written by Samuel Herrmann and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.

Stochastic resonance is a phenomenon arising in a wide spectrum of areas in the sciences ranging from physics through neuroscience to chemistry and biology. This book presents a mathematical approach to stochastic resonance which is based on a large deviations principle (LDP) for randomly perturbed dynamical systems with a weak inhomogeneity given by an exogenous periodicity of small frequency. Resonance, the optimal tuning between period length and noise amplitude, is explained by optimizing the LDP's rate function. The authors show that not all physical measures of tuning quality are robust with respect to dimension reduction. They propose measures of tuning quality based on exponential transition rates explained by large deviations techniques and show that these measures are robust. The book sheds some light on the shortcomings and strengths of different concepts used in the theory and applications of stochastic resonance without attempting to give a comprehensive overview of the many facets of stochastic resonance in the various areas of sciences. It is intended for researchers and graduate students in mathematics and the sciences interested in stochastic dynamics who wish to understand the conceptual background of stochastic resonance.

Effective Dynamics Of Stochastic Partial Differential Equations

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Author : Jinqiao Duan
language : en
Publisher: Elsevier
Release Date : 2014-03-06

Effective Dynamics Of Stochastic Partial Differential Equations written by Jinqiao Duan and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-06 with Mathematics categories.

Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors' experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. - New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty - Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations - Solutions or hints to all Exercises

Dynamical Systems Pdes And Networks For Biomedical Applications Mathematical Modeling Analysis And Simulations

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Author : André H. Erhardt
language : en
Publisher: Frontiers Media SA
Release Date : 2023-02-15

Dynamical Systems Pdes And Networks For Biomedical Applications Mathematical Modeling Analysis And Simulations written by André H. Erhardt 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 2023-02-15 with Science categories.

Local Lyapunov Exponents

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Author : Wolfgang Siegert
language : en
Publisher: Springer Science & Business Media
Release Date : 2009

Local Lyapunov Exponents written by Wolfgang Siegert 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 2009 with Language Arts & Disciplines categories.

Establishing a new concept of local Lyapunov exponents the author brings together two separate theories, namely Lyapunov exponents and the theory of large deviations. Specifically, a linear differential system is considered which is controlled by a stochastic process that during a suitable noise-intensity-dependent time is trapped near one of its so-called metastable states. The local Lyapunov exponent is then introduced as the exponential growth rate of the linear system on this time scale. Unlike classical Lyapunov exponents, which involve a limit as time increases to infinity in a fixed system, here the system itself changes as the noise intensity converges, too.

Geometry And Invariance In Stochastic Dynamics

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Author : Stefania Ugolini
language : en
Publisher: Springer Nature
Release Date : 2022-02-09

Geometry And Invariance In Stochastic Dynamics written by Stefania Ugolini and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-09 with Mathematics categories.

This book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications. The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications. The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie’s Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling.

Systemic Risk Tomography

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Author : Monica Billio
language : en
Publisher: Elsevier
Release Date : 2016-11-25

Systemic Risk Tomography written by Monica Billio and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-25 with Business & Economics categories.

In April 2010 Europe was shocked by the Greek financial turmoil. At that time, the global financial crisis, which started in the summer of 2007 and reached systemic dimensions in September 2008 with the Lehman Brothers' crash, took a new course. An adverse feedback loop between sovereign and bank risks reflected into bubble-like spreads, as if financial markets had received a wake-up call concerning the disregarded structural vulnerability of economies at risk.These events inspired the SYRTO project to "think and rethink the economic and financial system and to conceive it as an "ensemble of Sovereigns and Banks with other Financial Intermediaries and Corporations. Systemic Risk Tomography: Signals, Measurement and Transmission Channels proposes a novel way to explore the financial system by sectioning each part of it and analyzing all relevant inter-relationships. The financial system is inspected as a biological entity to identify the main risk signals and to provide the correct measures of prevention and intervention. - Explores the economic and financial system of Sovereigns, Banks, other Financial Intermediaries, and Corporations - Presents the financial system as a biological entity to be explored in order to identify the main risk signals and provide the right measures of prevention and interventions - Offers a new, systemic-based approach to construct a hierarchical, internally coherent framework to be used in developing an effective early warning system

The Science Of Hysteresis

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Author : Giorgio Bertotti
language : en
Publisher: Elsevier
Release Date : 2005-12-20

The Science Of Hysteresis written by Giorgio Bertotti and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-20 with Science categories.

Volume 1 covers: * Mathematical models * Differential equations * Stochastic aspects of hysteresis * Binary detection using hysteresis * Models of unemployment in economics Volume 2 covers: * Physical models of magnetic hysteresis * All aspects of magnetisation dynamics Volume 3 covers: * Hysteresis phenomena in materials* Over 2100 pages, rich with supporting illustrations, figures and equations * Contains contributions from an international list of authors, from a wide-range of disciplines * Covers all aspects of hysteresis - from differential equations, and binary detection, to models of unemployment and magnetisation dynamics