| Description |
1 online resource |
| Contents |
Preface; Contents; Introduction; 1 Optoisolation Circuits with Limit Cycles; 1.1 Optoisolation Circuits with Limit Cycles; 1.2 Optoisolation Circuits with Limit Cycles Stability Analysis; 1.3 Poincare-Bendixson Stability and Limit Cycle Analysis; 1.4 Optoisolation Circuits Poincare-Bendixson Analysis; 1.5 Optoisolation Nonlinear Oscillations Lienard Circuits; 1.6 Optoisolation Circuits with Weakly Nonlinear Oscillations; 1.7 Exercises; 2 Optoisolation Circuits Bifurcation Analysis (I); 2.1 Cusp Bifurcation Analysis System; 2.2 Optoisolation Circuits Cusp Bifurcation Analysis |
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2.3 Bautin Bifurcation Analysis System2.4 Optoisolation Circuits Bautin Bifurcation Analysis; 2.5 Bogdanov-Takens (Double-Zero) Bifurcation System; 2.6 Optoisolation Circuits Bogdanov-Takens (Double-Zero) Bifurcation; 2.7 Exercises; 3 Optoisolation Circuits Bifurcation Analysis (II); 3.1 Fold-Hopf Bifurcation System; 3.2 Optoisolation Circuits Fold-Hopf Bifurcation; 3.3 Hopf-Hopf Bifurcation System; 3.4 Optoisolation Circuits Hopf-Hopf Bifurcation System; 3.5 Neimark-Sacker (Torus) Bifurcation System; 3.6 Optoisolation Circuits Neimark-Sacker (Torus) Bifurcation; 3.7 Exercises |
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4 Optoisolation Circuits Analysis Floquet Theory4.1 Floquet Theory Basic Assumptions and Definitions; 4.2 Optoisolation Circuit's Two Variables with Periodic Sources; 4.3 Optoisolation Circuit's Two Variables with Periodic Sources Limit Cycle Stability; 4.4 Optoisolation Circuit Second-Order ODE with Periodic Source; 4.5 Optoisolation Circuit Second-Order ODE with Periodic Source Stability of a Limit Cycle; 4.6 Optoisolation Circuit Hills Equations; 4.7 Exercises; 5 Optoisolation NDR Circuits Behavior Investigation by Using Floquet Theory; 5.1 OptoNDR Circuit Floquet Theory Analysis |
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5.2 Chua's Circuit Fixed Points and Stability Analysis5.3 Chua's Circuit with OptoNDR Element Stability Analysis; 5.4 OptoNDR Circuit's Two Variables Analysis; 5.5 OptoNDR Circuit's Two Variables Analysis by Using Floquet Theory; 5.6 OptoNDR Circuit's Second-Order ODE with Periodic Source Stability of a Limit Cycle; 5.7 Exercises; 6 Optoisolation Circuits with Periodic Limit Cycle Solutions Orbital Stability; 6.1 Planar Cubic Vector Field and Van der Pol Equation; 6.2 OptoNDR Circuit Van der Pol Limit Cycle Solution; 6.3 Glycolytic Oscillator Periodic Limit Cycle and Stability |
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6.4 Optoisolation Glycolytic Circuits Limit Cycle Solution6.5 Exercises; 7 Optoisolation Circuits Poincare Maps and Periodic Orbit; 7.1 Poincare Maps and Periodic Orbit Flow; 7.2 Optoisolation van der pol Circuit Poincare Map and Periodic Orbit; 7.3 Li Dynamical System Poincare Map and Periodic Orbit; 7.4 OptoNDR Negative Differential Resistance (NDR) Oscillator Circuit Poincare Map and Periodic Orbit; 7.5 Exercises; 8 Optoisolation Circuits Averaging Analysis and Perturbation from Geometric Viewpoint; 8.1 Poincare Maps and Averaging; 8.2 OptoNDR Circuit van der Pol Perturbation Method |
| Summary |
This book on advanced optoisolation circuits for nonlinearity applications in engineering addresses two separate engineering and scientific areas, and presents advanced analysis methods for optoisolation circuits that cover a broad range of engineering applications. The book analyzes optoisolation circuits as linear and nonlinear dynamical systems and their limit cycles, bifurcation, and limit cycle stability by using Floquet theory. Further, it discusses a broad range of bifurcations related to optoisolation systems: cusp-catastrophe, Bautin bifurcation, Andronov-Hopf bifurcation, Bogdanov-Takens (BT) bifurcation, fold Hopf bifurcation, Hopf-Hopf bifurcation, Torus bifurcation (Neimark-Sacker bifurcation), and Saddle-loop or Homoclinic bifurcation. Floquet theory helps as to analyze advance optoisolation systems. Floquet theory is the study of the stability of linear periodic systems in continuous time. Another way to describe Floquet theory, it is the study of linear systems of differential equations with periodic coefficients. The optoisolation system displays a rich variety of dynamical behaviors including simple oscillations, quasi-periodicity, bi-stability between periodic states, complex periodic oscillations (including the mixed-mode type), and chaos. The route to chaos in this optoisolation system involves a torus attractor which becomes destabilized and breaks up into a fractal object, a strange attractor. The book is unique in its emphasis on practical and innovative engineering applications. These include optocouplers in a variety of topological structures, passive components, conservative elements, dissipative elements, active devices, etc. In each chapter, the concept is developed from the basic assumptions up to the final engineering outcomes. The scientific background is explained at basic and advanced levels and closely integrated with mathematical theory. The book is primarily intended for newcomers to linear and nonlinear dynamics and advanced optoisolation circuits, as well as electrical and electronic engineers, students and researchers in physics who read the first book "Optoisolation Circuits Nonlinearity Applications in Engineering". It is ideally suited for engineers who have had no formal instruction in nonlinear dynamics, but who now desire to bridge the gap between innovative optoisolation circuits and advanced mathematical analysis methods |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed June 1, 2017) |
| Subject |
Optoelectronic devices.
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Optoelectronics.
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Electric circuits.
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circuits.
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Laser technology & holography.
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Nonlinear science.
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Circuits & components.
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Microwave technology.
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TECHNOLOGY & ENGINEERING -- Mechanical.
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Electric circuits
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Optoelectronic devices
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Optoelectronics
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| Form |
Electronic book
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| ISBN |
9783319553160 |
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331955316X |
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