Weak-noise-induced Phenomena in a Slow-fast Dynamical System PDF Download
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Author: Marius Emar Yamakou
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Marius Emar Yamakou
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Nils Berglund
Publisher: Springer Science & Business Media
ISBN: 1846281865
Category : Mathematics
Languages : en
Pages : 283
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Book Description
Stochastic Differential Equations have become increasingly important in modelling complex systems in physics, chemistry, biology, climatology and other fields. This book examines and provides systems for practitioners to use, and provides a number of case studies to show how they can work in practice.
Author: Luca Ridolfi
Publisher: Cambridge University Press
ISBN: 1139498258
Category : Science
Languages : en
Pages : 327
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Book Description
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.
Author: Christian Kuehn
Publisher: Springer
ISBN: 3319123165
Category : Mathematics
Languages : en
Pages : 816
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Book Description
This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Author: André H. Erhardt
Publisher: Frontiers Media SA
ISBN: 2832514588
Category : Science
Languages : en
Pages : 209
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Book Description
Author: Jinqiao Duan
Publisher: Elsevier
ISBN: 0128012692
Category : Mathematics
Languages : en
Pages : 283
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Book Description
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
Author: Samuel Herrmann
Publisher: American Mathematical Soc.
ISBN: 1470410494
Category : Mathematics
Languages : en
Pages : 209
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Book Description
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.
Author: Stefania Ugolini
Publisher: Springer Nature
ISBN: 303087432X
Category : Mathematics
Languages : en
Pages : 273
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Book Description
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.
Author: Wolfgang Siegert
Publisher: Springer Science & Business Media
ISBN: 3540859632
Category : Mathematics
Languages : en
Pages : 264
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Book Description
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.
Author: Monica Billio
Publisher: Elsevier
ISBN: 0081011768
Category : Business & Economics
Languages : en
Pages : 302
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Book Description
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
