In This Chapter

Nonlinear Dynamics

Authored by: István Nagy , Zoltán Sütő

The Industrial Electronics Handbook

Print publication date:  February  2011
Online publication date:  April  2016

Print ISBN: 9781439802878
eBook ISBN: 9781439802885
Adobe ISBN:


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1.1 Introduction 1-1

1.2 Basics 1-2

ClassificationRestrictionsMathematical Description

1.3 Equilibrium Points 1-5

IntroductionBasin of AttractionLinearizing around the EPStabilityClassification of EPs, Three-Dimensional State Space (N = 3)No-Intersection Theorem

1.4 Limit Cycle 1-9

IntroductionPoincaré Map Function (PMF)Stability

1.5 Quasi-Periodic and Frequency-Locked State 1-12

IntroductionNonlinear Systems with Two FrequenciesGeometrical InterpretationN-Frequency Quasi-Periodicity

1.6 Dynamical Systems Described by Discrete-Time Variables: Maps 1-14

IntroductionFixed PointsMathematical ApproachGraphical ApproachStudy of Logistic MapStability of Cycles

1.7 Invariant Manifolds: Homoclinic and Heteroclinic Orbits 1-21

IntroductionInvariant Manifolds, CTMInvariant Manifolds, DTMHomoclinic and Heteroclinic Orbits, CTM

1.8 Transitions to Chaos 1-24

IntroductionPeriod-Doubling BifurcationPeriod-Doubling Scenario in General

1.9 Chaotic State 1-26

IntroductionLyapunov Exponent

1.10 Examples from Power Electronics 1-27

IntroductionHigh-Frequency Time-Sharing InverterDual Channel Resonant DC–DC ConverterHysteresis Current-Controlled Three-Phase VSCSpace Vector Modulated VSC with Discrete-Time Current ControlDirect Torque Control

Acknowledgments 1-41

References 1-41

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