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Introduction to nonlinear oscillations / Vladimir I. Nekorkin.

By: Publication details: Weinheim : Wiley-VCH, ©2015.Description: xi, 250 p. : illustrations ; 25 cmISBN:
  • 9783527413300
Subject(s): DDC classification:
  • 531.32 23 N418
Contents:
1. Introduction to the Theory of Oscillations -- 2. One-Dimensional Dynamics -- 3. Stability of Equilibria. A Classification of Equilibria of Two-Dimensional Linear Systems -- 4. Analysis of the Stability of Equilibria of Multidimensional Nonlinear Systems -- 5. Linear and Nonlinear Oscillators -- 6. Basic Properties of Maps -- 7. Limit Cycles -- 8. Basic Bifurcations of Equilibria in the Plane -- 9. Bifurcations of Limit Cycles. Saddle Homoclinic Bifurcation -- 10. The Saddle-Node Homoclinic Bifurcation. Dynamics of Slow-Fast Systems in the Plane -- 11. Dynamics of a Superconducting Josephson Junction -- 12. The Van der Pol Method. Self-Sustained Oscillations and Truncated Systems -- 13. Forced Oscillations of a Linear Oscillator -- 14. Forced Oscillations in Weakly Nonlinear Systems with One Degree of Freedom -- 15. Forced Synchronization of a Self-Oscillatory System with a Periodic External Force -- 16. Parametric Oscillations -- 17. Answers to Selected Exercises.
Summary: The text goes on to set out the basics of stability theory, as well as bifurcation theory in one and two-dimensional cases. Foundations of asymptotic methods and the theory of relaxation oscillations are presented, with much attention paid to a method of mappings and its applications.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 531.32 N418 (Browse shelf(Opens below)) Available 137193
Total holds: 0

Includes bibliographical references and index.

1. Introduction to the Theory of Oscillations --
2. One-Dimensional Dynamics --
3. Stability of Equilibria. A Classification of Equilibria of
Two-Dimensional Linear Systems --
4. Analysis of the Stability of Equilibria of Multidimensional Nonlinear Systems --
5. Linear and Nonlinear Oscillators --
6. Basic Properties of Maps --
7. Limit Cycles --
8. Basic Bifurcations of Equilibria in the Plane --
9. Bifurcations of Limit Cycles. Saddle Homoclinic Bifurcation --
10. The Saddle-Node Homoclinic Bifurcation. Dynamics of Slow-Fast Systems in the Plane --
11. Dynamics of a Superconducting Josephson Junction --
12. The Van der Pol Method. Self-Sustained Oscillations and Truncated Systems --
13. Forced Oscillations of a Linear Oscillator --
14. Forced Oscillations in Weakly Nonlinear Systems with One Degree of Freedom --
15. Forced Synchronization of a Self-Oscillatory System with a Periodic External Force --
16. Parametric Oscillations --
17. Answers to Selected Exercises.

The text goes on to set out the basics of stability theory, as well as bifurcation theory in one and two-dimensional cases. Foundations of asymptotic methods and the theory of relaxation oscillations are presented, with much attention paid to a method of mappings and its applications.

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