LEADER 02006nam 2200529 450 001 9910819096703321 005 20170918215804.0 010 $a1-4704-0723-X 035 $a(CKB)3360000000464494 035 $a(EBL)3113939 035 $a(SSID)ssj0000889221 035 $a(PQKBManifestationID)11478612 035 $a(PQKBTitleCode)TC0000889221 035 $a(PQKBWorkID)10876973 035 $a(PQKB)11177852 035 $a(MiAaPQ)EBC3113939 035 $a(RPAM)479551 035 $a(PPN)195411919 035 $a(EXLCZ)993360000000464494 100 $a20140909h19841984 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSpecial and spurious solutions of x(t) =-[alpha] f (x(t-1)) /$fRoger D. Nussbaum and Heinz-Otto Peitgen 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d1984. 210 4$d©1984 215 $a1 online resource (141 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vNumber 310 300 $a"September 1984, Volume 51, Number 310 (end of volume)." 311 $a0-8218-2311-6 320 $aIncludes bibliographical references. 327 $a""CONTENT""; ""0. INTRODUCTION""; ""1. PHASE PLANE STUDIES OF A CYCLIC SYSTEM""; ""2. CONTINUA OF SPECIAL PERIODIC SOLUTIONS""; ""3. NUMERICAL APPROXIMATION AND SPURIOUS SOLUTIONS""; ""4. A PRIORI BOUNDS WITHOUT THE ASSUMPTION OF ODDNESS""; ""REFERENCES"" 410 0$aMemoirs of the American Mathematical Society ;$vNumber 310. 606 $aDelay differential equations$xNumerical solutions 615 0$aDelay differential equations$xNumerical solutions. 676 $a515.3/52 700 $aNussbaum$b Roger D.$f1944-$056078 702 $aPeitgen$b Heinz-Otto$f1945- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910819096703321 996 $aSpecial and spurious solutions of x(t) =- f (x(t-1))$93971663 997 $aUNINA LEADER 05672nam 22006135 450 001 9910360849803321 005 20251113182159.0 010 $a3-030-32849-X 024 7 $a10.1007/978-3-030-32849-8 035 $a(CKB)4100000009939740 035 $a(DE-He213)978-3-030-32849-8 035 $a(MiAaPQ)EBC5989088 035 $a(PPN)242818668 035 $a(MiAaPQ)EBC5989015 035 $a(EXLCZ)994100000009939740 100 $a20191202d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBoundary Synchronization for Hyperbolic Systems /$fby Tatsien Li, Bopeng Rao 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2019. 215 $a1 online resource (X, 333 p. 2 illus., 1 illus. in color.) 225 1 $aPNLDE Subseries in Control,$x2731-7374 ;$v94 311 08$a3-030-32848-1 327 $aIntroduction and Overview -- Preliminaries -- Part 1: Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls: Exact Boundary Synchronization -- Exact boundary controllability and non-exact boundary controllability -- Exact boundary synchronization and non-exact boundary synchronization -- Exactly synchronizable states -- Exact boundary synchronization by groups -- Exactly synchronizable states by p-groups -- Part 2: Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls: Approximate Boundary Synchronization -- Approximate boundary synchronization -- Approximate boundary synchronization by p-groups -- Induced approximate boundary synchronization -- Part 3: Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls: Exact Boundary Synchronization -- Exact boundary controllability and non-exact boundary controllability -- Exact boundary synchronization and non-exactly boundary synchronization -- Exact boundary synchronization by p-groups -- Determination of exactly synchronizable states by p-groups -- Part 4: Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls: Approximate Boundary Synchronization -- Approximate boundary null controllability -- Approximate boundary synchronization -- Approximate Boundary Synchronization by p-groups -- Part 5: Synchronization for a Coupled System of Wave Equations with Coupled Robin Boundary Controls: Exact Boundary Synchronization -- Preliminaries on problem (III) and (III0) -- Exact boundary controllability and non-exact boundary controllability -- Exact boundary synchronization -- Determination of exactly synchronizable states -- Exact boundary synchronization by p-groups -- Necessity of the conditions of Cp-compatibility -- Determination of exactly synchronizable states by p-groups -- Part 6. Synchronization for a Coupled System of Wave Equations with Coupled Boundary Controls: Approximate Boundary Synchronization -- Some algebraic lemmas -- Approximate boundary null controllability -- Unique continuation for Robin problem -- Approximate boundary synchronization -- Approximate boundary synchronization by p-groups -- Approximately synchronizable states by p-groups -- Closing remarks. 330 $aWithin this carefully presented monograph, the authors extend the universal phenomenon of synchronization from finite-dimensional dynamical systems of ordinary differential equations (ODEs) to infinite-dimensional dynamical systems of partial differential equations (PDEs). By combining synchronization with controllability, they introduce the study of synchronization to the field of control and add new perspectives to the investigation of synchronization for systems of PDEs. With a focus on synchronization for a coupled system of wave equations, the text is divided into three parts corresponding to Dirichlet, Neumann, and coupled Robin boundary controls. Each part is then subdivided into chapters detailing exact boundary synchronization and approximate boundary synchronization, respectively. The core intention is to give artificial intervention to the evolution of state variables through appropriate boundary controls for realizing the synchronization in a finite time, creating a novel viewpoint into the investigation of synchronization for systems of partial differential equations, and revealing some essentially dissimilar characteristics from systems of ordinary differential equations. Primarily aimed at researchers and graduate students of applied mathematics and applied sciences, this text will particularly appeal to those interested in applied PDEs and control theory for distributed parameter systems. 410 0$aPNLDE Subseries in Control,$x2731-7374 ;$v94 606 $aSystem theory 606 $aControl theory 606 $aDifferential equations 606 $aAutomatic control 606 $aSystems Theory, Control 606 $aDifferential Equations 606 $aControl and Systems Theory 615 0$aSystem theory. 615 0$aControl theory. 615 0$aDifferential equations. 615 0$aAutomatic control. 615 14$aSystems Theory, Control. 615 24$aDifferential Equations. 615 24$aControl and Systems Theory. 676 $a519 700 $aLi$b Tatsien$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755910 702 $aRao$b Bopeng$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910360849803321 996 $aBoundary Synchronization for Hyperbolic Systems$92523259 997 $aUNINA