LEADER 05167nam 2200661Ia 450 001 9910144739203321 005 20170816120955.0 010 $a1-282-01051-4 010 $a9786612010514 010 $a3-527-61754-X 010 $a3-527-61755-8 035 $a(CKB)1000000000377428 035 $a(EBL)481556 035 $a(OCoLC)310355379 035 $a(SSID)ssj0000104762 035 $a(PQKBManifestationID)11130716 035 $a(PQKBTitleCode)TC0000104762 035 $a(PQKBWorkID)10085297 035 $a(PQKB)10711269 035 $a(MiAaPQ)EBC481556 035 $a(PPN)185148182 035 $a(EXLCZ)991000000000377428 100 $a19940622d1995 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aApplied nonlinear dynamics$b[electronic resource] $eanalytical, computational, and experimental methods /$fAli H. Nayfeh, Balakumar Balachandran 210 $aNew York $cWiley$dc1995 215 $a1 online resource (703 p.) 225 1 $aWiley series in nonlinear science 300 $a"A Wiley-Interscience publication." 311 $a0-471-59348-6 320 $aIncludes bibliographical references (p. 589-661) and index. 327 $aAPPLIED NONLINEAR DYNAMICS; CONTENTS; PREFACE; 1 INTRODUCTION; 1.1 DISCRETE-TIME SYSTEMS; 1.2 CONTINUOUS-TIME SYSTEMS; 1.2.1 Nonautonomous Systems; 1.2.2 Autonomous Systems; 1.2.3 Phase Portraits and Flows; 1.3 ATTRACTING SETS; 1.4 CONCEPTS OF STABILITY; 1.4.1 Lyapunov Stability; 1.4.2 Asymptotic Stability; 1.4.3 Poincare? Stability; 1.4.4 Lagrange Stability (Bounded Stability); 1.4.5 Stability Through Lyapunov Function; 1.5 ATTRACTORS; 1.6 COMMENTS; 1.7 EXERCISES; 2 EQUILIBRIUM SOLUTIONS; 2.1 CONTINUOUS-TIME SYSTEMS; 2.1.1 Linearization Near an Equilibrium Solution 327 $a2.1.2 Classification and Stability of Equilibrium Solutions2.1.3 Eigenspaces and Invariant Manifolds; 2.1.4 Analytical Construction of Stable and Unstable Manifolds; 2.2 FIXED POINTS OF MAPS; 2.3 BIFURCATIONS OF CONTINUOUS SYSTEMS; 2.3.1 Local Bifurcations of Fixed Points; 2.3.2 Normal Forms for Bifurcations; 2.3.3 Bifurcation Diagrams and Sets; 2.3.4 Center Manifold Reduction; 2.3.5 The Lyapunov-Schmidt Method; 2.3.6 The Method of Multiple Scales; 2.3.7 Structural Stability; 2.3.8 Stability of Bifurcations to Perturbations; 2.3.9 Codimension of a Bifurcation; 2.3.10 Global Bifurcations 327 $a2.4 BIFURCATIONS OF MAPS2.5 EXERCISES; 3 PERIODIC SOLUTIONS; 3.1 PERIODIC SOLUTIONS; 3.1.1 Autonomous Systems; 3.1.2 Nonautonomous Systems; 3.1.3 Comments; 3.2 FLOQUET THEORY; 3.2.1 Autonomous Systems; 3.2.2 Nonautonomous Systems; 3.2.3 Comments on the Monodromy Matrix; 3.2.4 Manifolds of a Periodic Solution; 3.3 POINCARE? MAPS; 3.3.1 Nonautonomous Systems; 3.3.2 Autonomous Systems; 3.4 BIFURCATIONS; 3.4.1 Symmetry-Breaking Bifurcation; 3.4.2 Cyclic-Fold Bifurcation; 3.4.3 Period-Doubling or Flip Bifurcation; 3.4.4 Transcritical Bifurcation; 3.4.5 Secondary Hopf or Neimark Bifurcation 327 $a3.5 ANALYTICAL CONSTRUCTIONS3.5.1 Method of Multiple Scales; 3.5.2 Center Manifold Reduction; 3.5.3 General Case; 3.6 EXERCISES; 4 QUASIPERIODIC SOLUTIONS; 4.1 POINCARE? MAPS; 4.1.1 Winding Time and Rotation Number; 4.1.2 Second-Order Poincare? Map; 4.1.3 Comments; 4.2 CIRCLE MAP; 4.3 CONSTRUCTIONS; 4.3.1 Method of Multiple Scales; 4.3.2 Spectral Balance Method; 4.3.3 Poincare? Map Method; 4.4 STABILITY; 4.5 SYNCHRONIZATION; 4.6 EXERCISES; 5 CHAOS; 5.1 MAPS; 5.2 CONTINUOUS-TIME SYSTEMS; 5.3 PERIOD-DOUBLING SCENARIO; 5.4 INTERMITTENCY MECHANISMS; 5.4.1 Type I Intermittency 327 $a5.4.2 Type III Intermittency5.4.3 Type II Intermittency; 5.5 QUASIPERIODIC ROUTES; 5.5.1 Ruelle-Takens Scenario; 5.5.2 Torus Breakdown; 5.5.3 Torus Doubling; 5.6 CRISES; 5.7 MELNIKOV THEORY; 5.7.1 Homoclinic Tangles; 5.7.2 Heteroclinic Tangles; 5.7.3 Numerical Prediction of Manifold Intersections; 5.7.4 Analytical Prediction of Manifold Intersections; 5.7.5 Application of Melnikov's Method; 5.7.6 Comments; 5.8 BIFURCATIONS OF HOMOCLINIC ORBITS; 5.8.1 Planar Systems; 5.8.2 Orbits Homoclinic to a Saddle; 5.8.3 Orbits Homoclinic to a Saddle Focus; 5.8.4 Comments; 5.9 EXERCISES 327 $a6 NUMERICAL METHODS 330 $aA unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincar? maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding. 410 0$aWiley series in nonlinear science. 606 $aDynamics 606 $aNonlinear theories 615 0$aDynamics. 615 0$aNonlinear theories. 676 $a515.35 676 $a621.38131 700 $aNayfeh$b Ali Hasan$f1933-$021715 701 $aBalachandran$b Balakumar$021716 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144739203321 996 $aApplied nonlinear dynamics$942543 997 $aUNINA