05167nam 2200661Ia 450 991014473920332120170816120955.01-282-01051-497866120105143-527-61754-X3-527-61755-8(CKB)1000000000377428(EBL)481556(OCoLC)310355379(SSID)ssj0000104762(PQKBManifestationID)11130716(PQKBTitleCode)TC0000104762(PQKBWorkID)10085297(PQKB)10711269(MiAaPQ)EBC481556(PPN)185148182(EXLCZ)99100000000037742819940622d1995 uy 0engur|n|---|||||txtccrApplied nonlinear dynamics[electronic resource] analytical, computational, and experimental methods /Ali H. Nayfeh, Balakumar BalachandranNew York Wileyc19951 online resource (703 p.)Wiley series in nonlinear science"A Wiley-Interscience publication."0-471-59348-6 Includes bibliographical references (p. 589-661) and index.APPLIED 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 Poincaré 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 Solution2.1.2 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 Bifurcations2.4 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 POINCARÉ 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 Bifurcation3.5 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 POINCARÉ MAPS; 4.1.1 Winding Time and Rotation Number; 4.1.2 Second-Order Poincaré 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 Poincaré 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 Intermittency5.4.2 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 EXERCISES6 NUMERICAL METHODSA 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.Wiley series in nonlinear science.DynamicsNonlinear theoriesDynamics.Nonlinear theories.515.35621.38131Nayfeh Ali Hasan1933-21715Balachandran Balakumar21716MiAaPQMiAaPQMiAaPQBOOK9910144739203321Applied nonlinear dynamics42543UNINA