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The Resource Analysis and Control of Complex Dynamical Systems : Robust Bifurcation, Dynamic Attractors, and Network Complexity

Analysis and Control of Complex Dynamical Systems : Robust Bifurcation, Dynamic Attractors, and Network Complexity

Label
Analysis and Control of Complex Dynamical Systems : Robust Bifurcation, Dynamic Attractors, and Network Complexity
Title
Analysis and Control of Complex Dynamical Systems
Title remainder
Robust Bifurcation, Dynamic Attractors, and Network Complexity
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Contributor
Subject
Language
eng
Summary
This book is the first to report on theoretical breakthroughs on control of complex dynamical systems developed by collaborative researchers in the two fields of dynamical systems theory and control theory. As well, its basic point of view is of three kinds of complexity: bifurcation phenomena subject to model uncertainty, complex behavior including periodic/quasi-periodic orbits as well as chaotic orbits, and network complexity emerging from dynamical interactions between subsystems. Analysis and Control of Complex Dynamical Systems offers a valuable resource for mathematicians, physicists, and biophysicists, as well as for researchers in nonlinear science and control engineering, allowing them to develop a better fundamental understanding of the analysis and control synthesis of such complex systems
Member of
Cataloging source
MiAaPQ
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Mathematics for Industry Ser.
Series volume
v.7
Analysis and Control of Complex Dynamical Systems : Robust Bifurcation, Dynamic Attractors, and Network Complexity
Label
Analysis and Control of Complex Dynamical Systems : Robust Bifurcation, Dynamic Attractors, and Network Complexity
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=2096072
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Copyright
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Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Preface -- Contents -- Part I Robust Bifurcation and Control -- 1 Dynamic Robust Bifurcation Analysis -- 1.1 Introduction -- 1.2 Problem Formulation: Dynamic Robust Bifurcation Analysis -- 1.3 Equilibrium, Stability/Instability, and Robustness Analysis -- 1.3.1 Equilibrium Analysis -- 1.3.2 Robust Hyperbolicity Analysis -- 1.3.3 Robust Bifurcation Analysis -- 1.4 Examples of Robust Bifurcation Analysis -- 1.4.1 Robustness Analysis of Saddle-Node Bifurcation -- 1.4.2 Robustness Analysis of Hopf Bifurcation -- 1.5 Conclusion -- References -- 2 Robust Bifurcation Analysis Based on Degree of Stability -- 2.1 Introduction -- 2.2 System Description and Robust Bifurcation Analysis -- 2.2.1 Continuous-Time Systems -- 2.2.2 Discrete-time Systems -- 2.2.3 Robust Bifurcation Analysis -- 2.3 Method of Robust Bifurcation Analysis -- 2.4 Numerical Examples -- 2.4.1 Equilibrium Point -- 2.4.2 Periodic Solution -- 2.5 Conclusion -- References -- 3 Use of a Matrix Inequality Technique for Avoiding Undesirable Bifurcation -- 3.1 Introduction -- 3.2 Considered Problem -- 3.3 Proposed Method -- 3.4 Extension -- 3.5 Example -- 3.6 Avoidance of Chaos -- 3.6.1 Method for Chaos Avoidance -- 3.6.2 Experimental Result -- 3.7 Conclusion -- References -- 4 A Method for Constructing a Robust System Against Unexpected Parameter Variation -- 4.1 Introduction -- 4.2 Method -- 4.2.1 Dynamical System -- 4.2.2 Search for Optimal Parameter Values -- 4.3 Results -- 4.3.1 Discrete-Time System -- 4.3.2 Continuous-Time System -- 4.4 Conclusion -- References -- 5 Parametric Control to Avoid Bifurcation Based on Maximum Local Lyapunov Exponent -- 5.1 Introduction -- 5.2 Problem Statement -- 5.3 Proposed Method -- 5.4 Experimental Results -- 5.5 Conclusion -- References -- 6 Threshold Control for Stabilization of Unstable Periodic Orbits in Chaotic Hybrid Systems -- 6.1 Introduction
  • 6.2 Design of Controller with Perturbation of the Threshold Value -- 6.3 A Simple Chaotic System -- 6.3.1 Numerical Simulation -- 6.3.2 Circuit Implementation -- 6.4 Izhikevich Model -- 6.4.1 Controller -- 6.4.2 Numerical Simulation -- 6.5 Conclusion -- References -- Part II Dynamic Attractor and Control -- 7 Chaotic Behavior of Orthogonally Projective Triangle Folding Map -- 7.1 Introduction -- 7.2 Orthogonally Projective Triangle Folding Map -- 7.3 Tetrahedron Map -- 7.3.1 Fixed Point and Periodic Point Analysis on the Boundary of mathcalD -- 7.4 Extended Fixed Point and Periodic Point Analysis for Tetrahedron Map -- 7.4.1 Geometric Interpretation of the Triangle Folding Map -- 7.4.2 Periodic Points of the Tetrahedron Map -- 7.4.3 Chaos by the Tetrahedron Map -- 7.5 Conclusion -- References -- 8 Stabilization Control of Quasi-periodic Orbits -- 8.1 Introduction -- 8.2 Properties of Quasi-periodic Orbit on Invariant Closed Curve -- 8.3 Unstable Quasi-periodic Orbit -- 8.4 External Force Control -- 8.5 Delayed Feedback Control -- 8.6 Pole Assignment Method -- 8.7 Conclusions -- References -- 9 Feedback Control Method Based on Predicted Future States for Controlling Chaos -- 9.1 Introduction -- 9.2 Method -- 9.3 Application -- 9.3.1 Logistic Map -- 9.3.2 Hénon Map -- 9.4 Conclusions -- References -- 10 Ultra-discretization of Nonlinear Control Systems with Spatial Symmetry -- 10.1 Introduction -- 10.2 Basic Properties on the Hexagonal Cellular Space -- 10.2.1 Coordinate Settings -- 10.2.2 Basics of Difference Calculus in Concern -- 10.3 Locomotion Under Nonholonomic Constraints -- 10.3.1 Derivation of the Continuous Single-Cart Model -- 10.3.2 Derivation of the Discrete Version -- 10.3.3 Holonomy and the Lie Bracket Motion -- 10.4 Connected Rigid Bodies: Locomotion Under both Nonholonomic and Holonomic Constraints -- 10.4.1 Cart-Trailer Systems
  • 10.4.2 Derivation of the Discrete Version -- 10.5 Reachability Issues -- 10.5.1 Definitions -- 10.5.2 Application -- 10.6 Other Possibilities of Cellular Tesselation -- 10.7 Conclusion -- References -- 11 Feedback Control of Spatial Patterns in Reaction-Diffusion Systems -- 11.1 Introduction -- 11.2 Pattern Formation by Global Feedback -- 11.2.1 Turing Instability -- 11.2.2 Interpretation of Turing Instability by Global Feedback -- 11.2.3 0:1:2-Mode Interaction -- 11.2.4 Wave Instability -- 11.2.5 Summary -- 11.3 Selective Stabilization of Turing Patterns -- 11.3.1 Reaction-Diffusion Systems -- 11.3.2 Problem Formulation -- 11.3.3 Feedback Control of Center Manifold Dynamics -- 11.3.4 Numerical Example -- 11.3.5 Summary -- References -- 12 Control of Unstabilizable Switched Systems -- 12.1 Introduction -- 12.2 Problem Formulation -- 12.2.1 Unstabilizable Switched Systems -- 12.2.2 Divergence Delay Problem -- 12.3 Discrete Abstraction of Switched Systems -- 12.4 Divergence Delay Control Based on Discrete Abstraction -- 12.5 Application to Optimal Scheduling Intermittent Androgen Suppression for Treatment of Prostate Cancer -- 12.5.1 Mathematical Model of ISA -- 12.5.2 Sub-optimal Scheduling Based on Discrete Abstraction -- 12.6 Conclusion -- References -- Part III Complex Networks and Modeling for Control -- 13 Clustered Model Reduction of Large-Scale Bidirectional Networks -- 13.1 Introduction -- 13.2 Preliminaries -- 13.3 Clustered Model Reduction -- 13.3.1 Problem Formulation -- 13.3.2 Exact Clustered Model Reduction -- 13.3.3 Approximation Error Evaluation for Clustered Model Reduction -- 13.4 Numerical Example: Application to Complex Networks -- 13.5 Conclusion -- References -- 14 Network Structure Identification from a Small Number of Inputs/Outputs -- 14.1 Introduction
  • 14.2 Characteristic-Polynomial-Based NW Structure Identification using Knock-Out -- 14.2.1 Problem Formulation -- 14.2.2 Representation Using the Generalized Frequency Variable -- 14.2.3 Identification Method -- 14.3 Identification of a Transfer Characteristic Among Measurable Nodes -- 14.3.1 Network System and Its Dynamical Structure Function -- 14.3.2 Reconstruction of Dynamical Structure Function from the Transfer Function of the NW System -- 14.4 Conclusions and Discussions -- References -- Index
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1 online resource (215 pages)
Form of item
online
Isbn
9784431550136
Media category
computer
Media MARC source
rdamedia
Media type code
c
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