Introduction to Nonlinear Oscillations
Blackwell Verlag GmbH (Hersteller)
978-3-527-69594-2 (ISBN)
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Since 2001 Vladimir Nekorkin is Head of the Laboratory of Dynamics of Nonequilibrium Media at the Novgorod State University. His expertise is in the areas of the dynamics of nonlinear systems, neurodynamics, nonlinear waves, and bifurcation theory.
INTRODUCTION TO THE THEORY OF OSCILLATIONS General Features of the Theory of Oscillations Dynamic Systems Attractors Structural Stability of Dynamic Systems Control Questions and Exercises ONE DIMENSIONAL DYNAMICS Qualitative Approach Rough Equilibria Bifurcations of Equilibria Systems on the Circle Control Questions and Exercises STABILITY OF EQUILIBRIA. A CLASSIFICATION OF EQUILIBRIA OF TWO-DIMENSIONAL LINEAR SYSTEMS Definition of the Stability of Equilibria Classification of Equilibria of Linear Systems on the Plane Control Questions and Exercises ANALYSIS OF THE STABILITY OF EQUILIBRIA OF MULTIDIMENSIONAL NONLINEAR SYSTEMS Linearization Method The Routh-Hurwitz Stability Criterion The Second Lyapunov Method Hyperbolic Equilibria of Three-Dimensional Systems Control Questions and Exercises LINEAR AND NONLINEAR OSCILLATORS The Dynamics of a Linear Oscillator Dynamics of a Nonlinear Oscillator Control Questions and Exercises BASIC PROPERTIES OF MAPS Point Maps as Models of Discrete Systems Poincare Map Fixed Points One-Dimensional Linear Maps Two-Dimensional Linear Maps One-Dimensional Nonlinear Maps: Some Notions and Examples Control Questions and Exercises LIMIT CYCLES Isolated and Nonisolated Periodic Trajectories. Definition of a Limit Cycle Orbital Stability. Stable and Unstable Limit Cycles Rotational and Librational Limit Cycles Rough Limit Cycles in Three-Dimensional Space The Bendixson-Dulac Criterion Control Questions and Exercises BASIC BIFURCATIONS OF EQUILIBRIA IN THE PLANE Bifurcation Conditions Saddle-Node Bifurcation The Andronov-Hopf Bifurcation Stability Loss Delay for the Dynamic Andronov-Hopf Bifurcation Control Questions and Exercises BIFURCATIONS OF LIMIT CYCLES. SADDLE HOMOCLINIC BIFURCATION Tangent Bifurcation of Limit Cycles Saddle Homoclinic Bifurcation Control Questions and Exercises THE SADDLE-NODE HOMOCLINIC BIFURCATION. DYNAMICS OF SLOW-FAST SYSTEMS IN THE PLANE Homoclinic Trajectory Final Remarks on Bifurcations of Systems in the Plane Dynamics of a Slow-Fast System Control Questions and Exercises DYNAMICS OF A SUPERCONDUCTING JOSEPHSON JUNCTION Stationary and Non-Stationary Effects Equivalent Circuit of the Junction Dynamics of the Model Control Questions and Exercises THE VAN DER POL METHOD. SELF-SUSTAINED OSCILLATIONS AND TRUNCATED SYSTEMS The Notion of Asymptotic Methods Self-Sustained Oscillations and Self-Oscillatory Systems Control Questions and Exercises FORCED OSCILLATIONS OF A LINEAR OSCILLATOR Dynamics of the System and the Global Poincare Map Resonance Curve Control Questions and Exercises FORCED OSCILLATIONS IN WEAKLY NONLINEAR SYSTEMS WITH ONE DEGREE OF FREEDOM Reduction of a System to the Standard Form Resonance in a Nonlinear Oscillator Forced Oscillation Regime Control Questions and Exercises FORCED SYNCHRONIZATION OF A SELF-OSCILLATORY SYSTEM WITH A PERIODIC EXTERNAL FORCE Dynamics of a Truncated System The Poincare Map and Synchronous Regime Amplitude-frequency Characteristic of a Self-Oscillatory System Control Questions and Exercises PARAMETRIC OSCILLATIONS The Floquet Theory Basic Regimes on Linear Parametric Systems Pendululm Dynamics with a Vibrating Suspension Point Oscillations of a Linear Oscillator with Slowly Variable Frequency Control Questions and Exercises
| Verlagsort | Berlin |
|---|---|
| Sprache | englisch |
| Maße | 150 x 250 mm |
| Gewicht | 666 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| Naturwissenschaften ► Physik / Astronomie ► Mechanik | |
| Technik ► Elektrotechnik / Energietechnik | |
| Technik ► Maschinenbau | |
| ISBN-10 | 3-527-69594-X / 352769594X |
| ISBN-13 | 978-3-527-69594-2 / 9783527695942 |
| Zustand | Neuware |
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