ALWAN - THEORY OF HYBRID SYSTEMS : deterministic and stochastic.

Nonlinear Physical Science

Nonlinear Physical Science focuses on recent advances of fundamental theories and principles, analytical and symbolic approaches, as well as computational techniques in nonlinear physical science and nonlinear mathematics with engineering applications.

Series editors

Albert C. J. Luo

Department of Mechanical and Industrial

Engineering

Southern Illinois University Edwardsville

Edwardsville, IL 62026-1805, USA

e-mail: aluo@siue.edu

Nail H. Ibragimov

Department of Mathematics and Science

Blekinge Institute of Technology

S-371 79 Karlskrona, Sweden

e-mail: nib@bth.se

International Advisory Board

Ping Ao, University of Washington, USA; Email: aoping@u.washington.edu

Jan Awrejcewicz, The Technical University of Lodz, Poland; Email: awrejcew@p.lodz.pl

Eugene Benilov, University of Limerick, Ireland; Email: Eugene.Benilov@ul.ie

Eshel Ben-Jacob, Tel Aviv University, Israel; Email: eshel@tamar.tau.ac.il

Maurice Courbage, Universit Paris 7, France; Email: maurice.courbage@univ-paris-diderot.fr

Marian Gidea, Northeastern Illinois University, USA; Email: mgidea@neiu.edu

James A. Glazier, Indiana University, USA; Email: glazier@indiana.edu

Shijun Liao, Shanghai Jiaotong University, China; Email: sjliao@sjtu.edu.cn

Jose Antonio Tenreiro Machado, ISEP-Institute of Engineering of Porto, Portugal; Email: jtm@isep.ipp.pt

Nikolai A. Magnitskii, Russian Academy of Sciences, Russia; Email: nmag@isa.ru

Josep J. Masdemont, Universitat Politecnica de Catalunya (UPC), Spain; Email: josep@barquins.upc.edu

Dmitry E. Pelinovsky, McMaster University, Canada; Email: dmpeli@math.mcmaster.ca

Sergey Prants, V.I.Ilichev Pacific Oceanological Institute of the Russian Academy of Sciences, Russia; Email: prants@poi.dvo.ru

Victor I. Shrira, Keele University, UK; Email: v.i.shrira@keele.ac.uk

Jian Qiao Sun, University of California, USA; Email: jqsun@ucmerced.edu

Abdul-Majid Wazwaz, Saint Xavier University, USA; Email: wazwaz@sxu.edu

Pei Yu, The University of Western Ontario, Canada; Email: pyu@uwo.ca

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Hybrid systems have become increasingly popular during the recent decades in various fields of the scientific research and are expected to carry on the potential for further explorations. A hybrid system exhibits a combination or coexistence of continuous and discrete events and has behaviors determined by the interaction between the continuous and discrete components, and/or between them with other environmental factors. From practical perspective, it has been observed that if the interaction, within a single system, is strong, then the above hybridness has to be unified in one model. This unification has paved the path to the study of hybrid systems leading to fascinating outcomes for the following reasons: (i) The hybrid system paradigm has been recognized as a proper tool to represent a wide range of diversified applications in nature or in the human-made world. Among those are systems modeling population growth model, infectious disease models, medical drugs, chemical reaction processes, heating/cooling systems, several control systems, power systems, automated highway systems, air traffic control systems, neural networks, computer synchronization, secure communication networks, just to name a few. (ii) A large class of systems are intrinsically ruled by multimodal dynamics, such as those presented in many control systems, multibody mechanical systems, thermostats in heating/cooling systems, preypredator systems with finite, different prey sources and epidemic disease models with periodic vaccinations or treatments. (iii) Many systems are asymptotically stabilized by multiple control laws monitored by a high-level supervisory agent, and others are stabilized or state estimated by discrete events. This is the case when the available information is only measured at discrete moments, rather than continuous time period, as in the case of vaccination or drugs administrated by way of injection. On the other hand, systems may undergo impulsive perturbing forces that must be taken into account in the modeling process. (iv) Nowadays, the technology has produced much hierarchically sophisticated machinery that cannot be analyzed as a whole system. Hybrid system representations can also be considered here to minimize the complexity of these systems. Namely, they provide sequential mathematical descriptions of the system that are often manageable for analysis. For these listed reasons, the heterogenous composition in the hybrid systems has become a modeling priority which, as a result, creates an important, fruitful research field applicable to many practical areas.