LEADER 04814nam 22007095 450 001 9910300532303321 005 20251107173104.0 010 $a3-319-93946-7 024 7 $a10.1007/978-3-319-93946-9 035 $a(CKB)4100000005323087 035 $a(DE-He213)978-3-319-93946-9 035 $a(MiAaPQ)EBC6283687 035 $a(PPN)229503071 035 $a(EXLCZ)994100000005323087 100 $a20180723d2018 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAdvances in Synchronization of Coupled Fractional Order Systems $eFundamentals and Methods /$fby Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XIX, 185 p. 66 illus., 59 illus. in color.) 225 1 $aUnderstanding Complex Systems,$x1860-0840 311 08$a3-319-93945-9 320 $aIncludes bibliographical references and index. 327 $aPreface -- Introduction -- Basic Concepts and Preliminares -- Synchronization of Chaotic Systems by means of a nonlinear observer: An application to Secure Communications -- Synchronization for Chaotic system through an Observer using the Immersion and Invariance (I&I) Approach -- Synchronization of Nonlinear Fractional Order Systems by Means of PIra Reduced Order Observer -- Estimators for a class of commensurate fractional order systems with Caputo derivative -- Generalized Multi-synchronization of Fractional Order Liouvillian Chaotic Systems using Fractional Dynamical Controller -- An Observer for a Class of Incommensurate Fractional Order Systems -- Fractional Generalized quasi-synchronization of incommensurate fractional order oscillators -- Synchronization and Anti-synchronization of fractional order chaotic systems by means of a fractional integral observer -- Appendix -- Index. 330 $aAfter a short introduction to the fundamentals, this book provides a detailed account of major advances in applying fractional calculus to dynamical systems. Fractional order dynamical systems currently continue to gain further importance in many areas of science and engineering. As with many other approaches to mathematical modeling, the first issue to be addressed is the need to couple a definition of the fractional differentiation or integration operator with the types of dynamical systems that are analyzed. As such, for the fundamentals the focus is on basic aspects of fractional calculus, in particular stability analysis, which is required to tackle synchronization in coupled fractional order systems, to understand the essence of estimators for related integer order systems, and to keep track of the interplay between synchronization and parameter observation. This serves as the common basis for the more advanced topics and applications presented in the subsequent chapters, which include an introduction to the 'Immersion and Invariance' (I&I) methodology, the masterslave synchronization scheme for partially known nonlinear fractional order systems, Fractional Algebraic Observability (FAO) and Fractional Generalized quasi-Synchronization (FGqS) to name but a few. This book is intended not only for applied mathematicians and theoretical physicists, but also for anyone in applied science dealing with complex nonlinear systems. . 410 0$aUnderstanding Complex Systems,$x1860-0840 606 $aMathematical physics 606 $aMultibody systems 606 $aVibration 606 $aMechanics, Applied 606 $aNonlinear Optics 606 $aDynamics 606 $aNonlinear theories 606 $aTheoretical, Mathematical and Computational Physics 606 $aMultibody Systems and Mechanical Vibrations 606 $aNonlinear Optics 606 $aApplied Dynamical Systems 615 0$aMathematical physics. 615 0$aMultibody systems. 615 0$aVibration. 615 0$aMechanics, Applied. 615 0$aNonlinear Optics. 615 0$aDynamics. 615 0$aNonlinear theories. 615 14$aTheoretical, Mathematical and Computational Physics. 615 24$aMultibody Systems and Mechanical Vibrations. 615 24$aNonlinear Optics. 615 24$aApplied Dynamical Systems. 676 $a515.83 700 $aMarti?nez-Guerra$b Rafael$4aut$4http://id.loc.gov/vocabulary/relators/aut$00 702 $aPérez-Pinacho$b Claudia Alejandra$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300532303321 996 $aAdvances in Synchronization of Coupled Fractional Order Systems$92525354 997 $aUNINA