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Jérôme Losson Michael C. Mackey Richard Taylor Marta Tyran-Kamińska

Density Evolution Under Delayed Dynamics An Open Problem

Fields Institute Monographs VOLUME 38 The Fields Institute for Research in Mathematical Sciences Fields Institute Editorial Board: Kumar Murty, Director Deirdre Haskell, Deputy Director of the Institute James G. Arthur, University of Toronto Kenneth R. Davidson, University of Waterloo Lisa Jeffrey, University of Toronto Barbara Lee Keyfitz, Ohio State University Thomas S. Salisbury, York University Noriko Yui, Queen’s University Juris Steprans, York University

The Fields Institute is a centre for research in the mathematical sciences, located in Toronto, Canada. The Institutes mission is to advance global mathematical activity in the areas of research, education and innovation. The Fields Institute is supported by the Ontario Ministry of Training, Colleges and Universities, the Natural Sciences and Engineering Research Council of Canada, and seven Principal Sponsoring Universities in Ontario (Carleton, McMaster, Ottawa, Queen’s, Toronto, Waterloo, Western and York), as well as by a growing list of Affiliate Universities in Canada, the U.S. and Europe, and several commercial and industrial partners.

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Jérôme Losson • Michael C. Mackey Richard Taylor • Marta Tyran-Kami´nska

Density Evolution Under Delayed Dynamics An Open Problem

Jérôme Losson BC Partners London, UK Richard Taylor Department of Mathematics and Statistics Thompson Rivers University Kamloops, BC, Canada

Michael C. Mackey Department of Physiology McGill University Montreal, QC, Canada Marta Tyran-Kami´nska Institute of Mathematics University of Silesia Katowice, Poland

ISSN 1069-5273 ISSN 2194-3079 (electronic) Fields Institute Monographs ISBN 978-1-0716-1071-8 ISBN 978-1-0716-1072-5 (eBook) https://doi.org/10.1007/978-1-0716-1072-5 © Springer Science+Business Media, LLC, part of Springer Nature 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms 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 specific 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, expressed or implied, with respect to the material contained herein or for any