Discrete Dynamics And Difference Equations: Proceedings Of The Twelfth International Conference On Difference Equations And Applications

Elaydi Oliveira Ferreira Alves DISCRETE DYNAMICS AND DIFFERENCE EQUATIONS Proceedings of the Twelfth International Conference on Difference Equations and Applications The volume encompasses current topics on stability and bifurcation, chaos, mathematical biology, iteration theory, nonautonomous systems, and stochastic dynamical systems. World Scientific www.worldscientific.com 7470 hc 7470.09.Rok Ting.ML3.indd 1 ISBN-13 978-981-4287-64-7 ISBN-10 981-4287-64-4 ,!7IJ8B4-cihgeh! DISCRETE DYNAMICS AND DIFFERENCE EQUATIONS This volume holds a collection of articles based on the talks presented at ICDEA 2007 in Lisbon, Portugal. Proceedings of the Twelfth International Conference on Difference Equations and Applications Saber N Elaydi • Henrique Oliveira José Manuel Ferreira • João F Alves Editors World Scientific 9/30/10 5:20 PM This page is intentionally left blank 7470tp.indd 1 10/1/10 8:39 AM Proceedings of the Twelfth International Conference on Difference Equations and Applications Lisbon, Portugal, 23 – 27 July 2007 Saber N Elaydi Trinity University, USA Henrique Oliveira • José Manuel Ferreira • João F Alves Instituto Superior Técnico, Portugal Editors World Scientific NEW JERSEY 7470tp.indd 2 • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TA I P E I • CHENNAI 10/1/10 8:39 AM Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. DISCRETE DYNAMICS AND DIFFERENCE EQUATIONS Proceedings of the Twelfth International Conference on Difference Equations and Applications Copyright © 2010 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-13 978-981-4287-64-7 ISBN-10 981-4287-64-4 Printed in Singapore. RokTing - Discrete Dynamics.pmd 1 12/29/2010, 11:20 AM September 7, 2010 12:20 WSPC - Proceedings Trim Size: 9in x 6in dedication v Jos´e de Sousa Ramos (1948–2007) Jos´e Sousa Ramos was the main supporter of the idea of organizing the International Conference on Difference Equations and Applications 2007 in Lisbon, at the Instituto Superior T´ecnico. The ICDEA, jointly with ECIT (European Conference on Iteration Theory) were the conferences that he most enjoyed to attend. Unfortunately he deceased January 1, 2007, and therefore could not play the role that he had planned in the organization of this Conference. Sousa Ramos had a first degree in Physics and obtained his Ph.D. in Mathematics. In these sciences he showed a huge knowledge and a particular capacity of analyzing physical phenomena into the mathematical framework. He had a very creative and autonomous mind. This often led him to rather original ideas and very different and interesting ways of looking at sever