Preface

Abstract

The International Workshop on Multi-Rate Processes and Hysteresis conference series focuses on singular perturbation problems and hysteresis as common strongly nonlinear phenomena occurring in mathematical, physical, economical, engineering and information systems. The term ‘strongly nonlinear’ means, in particular, that linearization will not encapsulate the observed phenomena. Singular perturbation problems and hysteresis can be manifested at different stages of the same or similar processes. Furthermore, a number of fundamental hysteresis models can be considered as a limit of time relaxation processes, or admit an approximation by a differential equation, which is singular with respect to a particular parameter. However, interaction between researchers in the areas of systems with time relaxation and systems with hysteresis (and between the ‘multi-rate’ and ‘hysteresis’ research communities) has so far been limited, and there is little cross-fertilization of ideas. It is the aim of the conference series to fill this gap.The 5th International Workshop on Multi-Rate Processes and Hysteresis (MURPHYS 2010) was hosted by the Pollack Mihály Faculty of Engineering, University of Pécs, Hungary, from 31 May to 3 June 2010, on the occasion of Pécs being the Cultural Capital of Europe in 2010. The workshop was organized in cooperation with University College Cork, Ireland, which hosted all of the previous Workshops: International Workshop on Multi-rate Processes and Hysteresis (University College, Cork, Ireland, 31 March–5 April 2008). Proceedings are published in Journal of Physics: Conference Series volume 138. See http://euclid.ucc.ie/appliedmath/murphys2008/murphys2008.htm; International Workshop on Multi-rate Processes and Hysteresis (University College, Cork, Ireland, 3–8 April 2006). Proceedings are published in Journal of Physics: Conference Series volume 55. Further information is available at http://Euclid.ucc.ie/murphys2006.htm; International Workshop on Hysteresis and Multi-scale Asymptotic (University College, Cork, Ireland, 17–21 March 2004). Proceedings are published in Journal of Physics: Conference Series volume 22. Further details are available at http://Euclid.ucc.ie/hamsa2004.htm; International Workshop on Relaxation Oscillations and Hysteresis (University College, Cork, Ireland, 1–6 April 2002). The related collection of invited lectures was published as a volume Singular Perturbations and Hysteresis, SIAM, Philadelphia, 2005. International Workshop on Geometrical Methods of Nonlinear Analysis and Semiconductor Laser Dynamics (University College Cork, Ireland, 5–6 April 2001). A collection of invited papers has been published as a special issue of Proceedings of the Russian Academy of Natural Sciences: Nonlinear dynamics of laser and reacting system, available at http://euclid.ucc.ie/appliedmath/gmna2001/ProcGMNA2001p1.pdf. Among the aims of this and previous workshops were: to bring together the leading experts in singular perturbation and hysteresis phenomena in applied problems; to discuss important problems in the areas of reacting systems, semiconductor lasers, shock phenomena, economic modelling, fluid mechanics, electrical engineering and modelling biological systems with emphasises on hysteresis and singular perturbations; to learn and share modern techniques in areas of common interest. The International Workshop on Multi-rate Processes and Hysteresis (Pollack Mihály Faculty of Engineering, University of Pécs, Hungary, 31 May–3 June 2010) brought together about 50 scientists who are actively researching the areas of dynamical systems with hysteresis and singular perturbations with applications to physical, engineering and economic systems. The countries represented at the Workshop included the Czech Republic, Germany, Hungary, Ireland, Israel, Italy, Poland, Romania, Russia, the United Kingdom and USA. Workshop photo 31 May 2010 Sponsorship of the Workshop by the Pollack Mihály Faculty of Engineering, University of Pécs (Hungary), University College Cork (Ireland), University of Pécs (Hungary), The University of Texas at Dallas (USA), and the Cultural Capital of Europe 2010, Pécs (Hungary), is gratefully acknowledged.The Editors and Organizers of the Workshop are sincerely grateful to Dr Géza Várady, Ms Andrea Zseni and Mr Ádám Schiffer of the Pollack Mihály Faculty of Engineering, University of Pécs, and Dr Alexander Pimenov of University College Cork for managing the organization of the conference and for the assistance in formatting of all the manuscripts.More information about the workshop can be found at http://murphys5.pmmk.pte.hu/Amalia Ivanyi, Péter Iványi, Dmitrii Rachinskii and Vladimir A Sobolev EditorsMURPHYS 2010, PMMK PTE, 31 May – 3 June 2010Sponsored by POLLACK MIHÁLY FACULTY OF ENGINEERING, UNIVERSITY OF PÉCS PÉCSI TUDOMÁNYEGYETEM UNIVERSITY OF PÉCS Cultural Capital of Europe 2010, Pécs, Hungary International Steering Committee Z I BalanovIsrael M BrokateGermany R CrossUK K DahmenUSA M DimianRomania G FriedmanUSA A Ivanyi (Co-Chairman)Hungary P Iványi (Co-Chairman)Hungary L KalachevUSA P KrejčíCzech Republic R O'Malley (Co-Chairman)USA A Pokrovskii (Co-Chairman)Ireland N PopovicUK D Rachinskii (Co-Chairman)Ireland S S SazhinUK V Sobolev (Co-Chairman)Russia S SzabóHungary C VisoneItalyInternational Program Committee G AlmásiHungary Z BalanovIsrael M BrokateGermany R CrossUK K DahmenUSA M DimianRomania G FriedmanUSA A Ivanyi (Co-Chairman)Hungary P Iványi (Co-Chairman)Hungary S JeneiHungary G KádárHungary L KalachevUSA R KersnerHungary G KovácsHungary P KrejčíCzech Republic P M KuczmannHungary P P O'KaneIreland R O'Malley (Co-Chairman)USA A Pokrovskii (Co-Chairman)Ireland N PopovicUK D Rachinskii (Co-Chairman)Ireland B V H ToppingUK V C VisoneItaly