Stochastic effects in nonlinear systems
Oscillations are a frequently studied phenomenon in science. Examples of this widespread behaviour range from economy to natural sciences. Neurons also exhibit oscillatory properties. The Hodgkin-Huxley model [46] and the FitzHughNagumo model [47, 48] bel
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Springer awards „BestMasters“ to the best master’s theses which have been completed at renowned universities in Germany, Austria, and Switzerland. The studies received highest marks and were recommended for publication by supervisors. They address current issues from various fields of research in natural sciences, psychology, technology, and economics. The series addresses practitioners as well as scientists and, in particular, offers guidance for early stage researchers.
Paul M. Geffert
Stochastic Non-Excitable Systems with Time Delay Modulation of Noise Effects by Time-Delayed Feedback Foreword by Prof. Dr. Eckehard Schöll, PhD
Paul M. Geffert London, United Kingdom
BestMasters ISBN 978-3-658-09294-8 ISBN 978-3-658-09295-5 (eBook) DOI 10.1007/978-3-658-09295-5 Library of Congress Control Number: 2015933640 Springer Spektrum © Springer Fachmedien Wiesbaden 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, speci¿cally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on micro¿lms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a speci¿c statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer Spektrum is a brand of Springer Fachmedien Wiesbaden Springer Fachmedien Wiesbaden is part of Springer Science+Business Media (www.springer.com)
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Foreword Stochastic effects in nonlinear dynamical systems are an important field of stateof-the-art research. The interplay of noise, nonlinearity, and time-delayed feedback leads to a wealth of novel, unexpected phenomena, such as stochastic bifurcations, coherence resonance, etc. Stochastic bifurcation denotes the transition from a monomodal to a bimodal stationary probability distribution, and coherence resonance is a counterintuitive effect which describes the nonmonotonic dependence of the coherence of noise-induced oscillations upon noise strength, resulting in an optimum coherence at non-zero noise strength. This Master Thesis focusses on these effects in a simple paradigmatic model, i.e., the Stuart-Landau oscillator. The model variant which is considered in this thesis arises from the generic expansion of an oscillator system near a subcritical Hopf bifurcation in terms of a fif
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