| Description |
viii, 126 pages : illustrations ; 23 cm |
| Contents |
PREFACE; CONTENTS; Chapter 1; 1. HOPF BIFURCATION PROBLEM: AN ANALYTICAL APPROACH; 1.1. Introduction; 1.2. One Parameter Hopf Bifurcation; 1.3. Biparameter Hopf Bifurcation; 1.4. Bifurcation into Quasiperiodic Torus; 1.5. Hopf Bifurcation in Duffing's Oscillator; 1.5.1. A vibrating system; 1.5.2. Non-resonance case; 1.5.3. Main resonance; 1.5.4 Resonance of the n-th order; 1.5.5. Concluding remarks; 1.6. Hopf Bifurction in Nonstationary Nonlinear Systems; 1.6.1. Example without external force; 1.6.2. Example including external force; 1.6.3. Concluding remarks; Chapter 2 |
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2. BIFURCATION AND CHAOS: NUMERICAL METHOD BASED ON SOLVING BOUNDARY VALUE PROBLEM2.1. Introduction; 2.2. Gradual and Sudden Transition to Chaos; 2.2.1. Method and results; 2.2.2. Conclusions; 2.3. Three Different Routes Leading to Chaos; 2.3.1 . Period doubling bifurcation; 2.3.2. A particular oscillator with three equilibria; 2.3.3. Oscillator with a particular exciting force; 2.3.4. Concluding remarks; 2.4. Bifurcation of the Oscillations of Vocal Cords; Chapter 3; 3. CHAOS AFTER BIFURCATION OF PERIODIC AND QUASIPERIODIC ORBITS; 3.1. Introduction |
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3.2. Oscillator with a Static Load and Particular Exciting Force3.2.1. Bifurcation of periodic orbit with one frequency; 3.2.2. Bifurcation of the quasiperiodic orbit with two frequencies; 3.2.3. Summary and concluding remarks; 3.3. Particular Van der Pol-Duffing's Oscillator; 3.3.1. The analysed systems and averaged equations; 3.3.2. ""0""-type bifurcations; 3.3.3. Bifurcation of the periodic orbit; 3.3.4. Observations of strange chaotic attractors; 3.4. Oscillator with Delay; 3.4.1. Bifurcation of the periodic orbit; 3.4.2. Further observation of chaotic behaviour; References; Subject Index |
| Summary |
This book presents a detailed analysis of bifurcation and chaos in simple non-linear systems, based on previous works of the author. Practical examples for mechanical and biomechanical systems are discussed. The use of both numerical and analytical approaches allows for a deeper insight into non-linear dynamical phenomena. The numerical and analytical techniques presented do not require specific mathematical knowledge |
| Notes |
Includes index |
| Bibliography |
Includes bibliographical references (pages 115-120) and index |
| Notes |
English |
| Subject |
Bifurcation theory -- Numerical solutions
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Bifurcation theory.
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Boundary value problems.
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Boundary value problems -- Numerical solutions.
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Chaotic behavior in systems.
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| LC no. |
89022433 |
| ISBN |
9810200382 |
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