| Description |
1 online resource (492 p.) |
| Contents |
Intro -- Preface -- Acknowledgments -- Contents -- About the Author -- 1 Introduction -- 1.1 Brief Review of Nonlinear Ordinary Differential Equations -- 1.2 Brief Review of Differential Equations with Time Delay -- 1.3 Main Challenge of Study on Nonlinear Dynamics of Systems with Time Delay -- 1.3.1 Nonlinear Dynamics of Time Delay Systems -- 1.3.2 Methods of Solving Nonlinear Systems with Time Delay -- 1.3.3 Identification of Nonlinear Systems with Time Delay -- 1.3.4 Utilization of Time Delay in Vibration Suppression -- 1.3.5 Other Applications in the Presence of Time Delay |
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1.4 Structure of the Book -- References -- 2 Delay Induced Nonlinear Dynamics -- 2.1 Asymptotic Analytical Method for Periodic Solution of the Delay Induced VDP-Duffing System -- 2.1.1 Hopf Bifurcation and Btability Bwitching -- 2.1.2 Reduction on Center Manifold -- 2.1.3 The Phase-Shifting and Phase-Locked Periodic Solutions -- 2.2 1:3 Resonant Double Hopf Bifurcation in a Delayed Coupled VDP System -- 2.2.1 Multi-scale Analysis for 1:3 Resonance Double Hopf Bifurcation -- 2.2.2 1:3 Resonance Analysis of Time Delay Coupled VDP Oscillator System -- 2.2.3 Numerical Simulation |
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2.3 Multistability and Attraction Basin of VDP-Duffing System with Delayed Feedback -- 2.3.1 Mathematical Model -- 2.3.2 Approximated Analytical Solution of Periodic Solution -- 2.3.3 Basin of Attraction for Periodic Solutions of Multiple Steady States -- 2.4 Quasi-Periodic Solutions and Chaos in Time Delay Systems -- References -- 3 Perturbation-Incremental Scheme and Integral Equation Method for Solving Time Delay Systems -- 3.1 Perturbation-Incremental Scheme for Studying Hopf Bi-Furcation in Delay Differential Systems -- 3.1.1 Introduction -- 3.1.2 Perturbation-Incremental Scheme |
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3.1.3 Synchronization Solution in a Network of Three Identical Neurons -- 3.2 Perturbation-Incremental Scheme for Studying Weak Resonant Double Hopf Bifurcation of Nonlinear Systems with Time Delay -- 3.2.1 Weak Resonant Double Hopf Bifurcation -- 3.2.2 Perturbation-Incremental Scheme -- 3.2.3 Weak Resonant Double Hopf Bifurcation in the Van Der Pol-Duffing System with Delayed Feedback -- 3.3 Integral Equation Method for Nonlinear Systems with Time Delay -- 3.3.1 The Integral Equation Method -- 3.3.2 The Primary Resonance and 1:1 Internal Resonance of a Two-Degrees-of-Freedom Model -- Appendix |
| Summary |
This book presents research advancements in the dynamics of systems with time delay conducted by the group led by Professor Jian Xu. Addressing the challenges arising from the joint impact of time delay and nonlinearity, novel theoretical approaches are developed to formulate the nonlinear response of the system. This facilitates the classification of complex nonlinear dynamics, especially the non-resonant and resonant double Hopf bifurcation. In contrast to systems without time delay, time delay systems require specific considerations when identifying system parameters, particularly the time delay. Consequently, inverse problems of systems with time delay are also explored in this book. Moreover, detailed investigations on vibration suppression methods and experimental prototypes based on time delay, such as time delay isolators with quasi-zero stiffness, are conducted. Simultaneously, this book is enriched with a large number of case studies ranging from manufacturing, network science, biology, and public transportation, illuminating the mechanisms of delay-induced nonlinear dynamics in practical applications. This book is suitable for graduate students and researchers who are eager to understand the delay-induced nonlinear dynamics, or technical personnel in whose projects small variations of time delay may cause significant changes in system responses. |
| Bibliography |
References -- 4 Inverse Problem of Systems with Time Delay -- 4.1 Characteristics of Time Delay in the Frequency Domain -- 4.2 Parameter Identification for Linear Time Delay Systems -- 4.2.1 Qualitative Identification for Large Time Delays -- 4.2.2 Quantitative Identification for Practical Applications -- 4.2.3 Uniqueness in Delay Identification and Its Solution -- 4.3 Parameter Identification for Nonlinear Time Delay Systems -- 4.3.1 Algorithm Construction in Frequency Domain: Quasi-Linear Method -- 4.3.2 Algorithm Construction in Frequency Domain: Harmonic Balance Method |
| Notes |
4.4 Algorithm Modification for Noise-Correction Identification |
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Online resource; title from PDF title page (SpringerLink, viewed February 26, 2024) |
| Subject |
Time delay systems.
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Nonlinear mechanics.
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| Genre/Form |
Electronic books
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| Form |
Electronic book
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| ISBN |
9789819999071 |
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9819999073 |
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