Balachandran / Kalmár-Nagy / Gilsinn Delay Differential Equations

Recent Advances and New Directions
2009
ISBN: 978-0-387-85595-0
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 350 Seiten

Delay Differential Equations: Recent Advances and New Directions cohesively presents contributions from leading experts on the theory and applications of functional and delay differential equations (DDEs). Students and researchers will benefit from a unique focus on theory, symbolic, and numerical methods, which illustrate how the concepts described can be applied to practical systems ranging from automotive engines to remote control over the Internet. Comprehensive coverage of recent advances, analytical contributions, computational techniques, and illustrative examples of the application of current results drawn from biology, physics, mechanics, and control theory. Students, engineers and researchers from various scientific fields will find Delay Differential Equations: Recent Advances and New Directions a valuable reference.

Autoren/Hrsg.

Kalmár-Nagy, Tamás

Balachandran., Balakumar

Balachandran, Balakumar

Gilsinn, David E.

Inhaltsverzeichnis

1;Preface;5
2;Contents;8
3;Contributors;14
4;Lyapunov–Krasovskii Functional Approach for Coupled Differential-Difference Equations with Multiple Delays;16
4.1;1.1 Introduction;16
4.2;1.2 Coupled Differential-Functional Equations;20
4.3;1.3 Stability of Continuous Time Difference Equations;25
4.4;1.4 Linear Coupled Differential-Difference Equations;28
4.5;1.5 Discussion and Examples;38
4.6;1.6 Concluding Remarks;42
4.7;References;43
5;Networked Control and Observation for Master–Slave Systems;46
5.1;2.1 Introduction;46
5.2;2.2 Exponential Stability of a Remote System Controlled Through Internet;48
5.3;2.3 Architecture of the Global Control System;53
5.4;2.4 Performance Enhancement by a Gain Scheduling Strategy;60
5.5;2.5 Conclusion;66
5.6;References;67
6;Developments in Control of Time-Delay Systems for Automotive Powertrain Applications;69
6.1;3.1 Introduction;69
6.2;3.2 Idle Speed Control;70
6.3;3.3 Air-to-Fuel Ratio Control;77
6.4;3.4 Observer Design for a Diesel Engine Model with Time Delay;92
6.5;3.5 Concluding Remarks;102
6.6;Appendix: Robust and Stochastic Stability;103
6.7;References;104
7;Stability Analysis and Control of Linear Periodic Delayed Systems Using Chebyshev and Temporal Finite Element Methods;107
7.1;4.1 Introduction;107
7.2;4.2 Stability of Autonomous and Periodic DDEs;110
7.3;4.3 Temporal Finite Element Analysis;111
7.4;4.4 Chebyshev Polynomial Expansion and Collocation;118
7.5;4.5 Application to Milling Stability;127
7.6;4.6 Control of Periodic Systems with Delay using Chebyshev Polynomials;130
7.7;4.7 Discussion of Chebyshev and TFEA Approaches;137
7.8;References;140
8;Systems with Periodic Coefficients and Periodically Varying Delays: Semidiscretization-Based Stability Analysis;144
8.1;5.1 Introduction;144
8.2;5.2 Stability Analysis of Systems with Periodically Varying Delays;146
8.3;5.3 Approximation of the Monodromy Matrix by using the Semidiscretization Method;148
8.4;5.4 Applications;151
8.5;5.5 Closure;164
8.6;References;165
9;Bifurcations, Center Manifolds, and Periodic Solutions;167
9.1;6.1 Background;167
9.2;6.2 Decomposing Ordinary Differential Equations Using Adjoints;172
9.3;6.3 An Example Application in Ordinary Differential Equations;176
9.4;6.4 Delay Differential Equations as Operator Equations;179
9.5;6.5 A Machine Tool DDE Example: Part 1;188
9.6;6.6 Computing the Bifurcated Periodic Solution on the Center Manifold;198
9.7;6.7 A Machine Tool DDE Example: Part 2;202
9.8;6.8 Simulation Results;208
9.9;References;213
10;Center Manifold Analysis of the Delayed Li´enard Equation;215
10.1;7.1 Introduction;215
10.2;7.2 Linear Stability Analysis;216
10.3;7.3 Operator Differential Equation Formulation;218
10.4;7.4 Center Manifold Reduction;221
10.5;7.5 Hopf Bifurcation Analysis;224
10.6;7.6 Numerical Results;225
10.7;7.7 Hopf Bifurcation in the Sunflower Equation;226
10.8;7.8 Concluding Remarks;230
10.9;References;230
11;Calculating Center Manifolds for Delay Differential Equations Using MapleTM;232
11.1;8.1 Introduction;232
11.2;8.2 Theory;233
11.3;8.3 Application;241
11.4;8.4 Discussion;251
11.5;References;253
12;Numerical Solution of Delay Differential Equations;256
12.1;9.1 Introduction;256
12.2;9.2 DDEs are not ODEs;258
12.3;9.3 Numerical Methods and Software Issues;263
12.4;9.4 Examples;269
12.5;9.5 Conclusion;280
12.6;9.6 Further Reading;280
12.7;References;280
13;Effects of Time Delay on Synchronization and Firing Patterns in Coupled Neuronal Systems;283
13.1;10.1 Introduction;283
13.2;10.2 Basic Concepts;286
13.3;10.3 Synchronization and Firing Patterns in Electrically Coupled Neurons with Time Delay;290
13.4;10.4 Synchronization and Firing Patterns in Coupled Neurons with Delayed Inhibitory Synapses;293
13.5;10.5 Synchronization and Firing Patterns in Coupled Neurons with Delayed Excitatory Synapses;299
13.6;10.6 Delay Effect on Multistability and Spatiotemporal Dynamics of Coupled Neuronal Activity [14];302
13.7;10.7 Closure;307
13.8;Appendix 10.1 The Hodgkin–Huxley (HH) Model;309
13.9;Appendix 10.2 The Morris–Lecar(ML) Model;310
13.10;Appendix 10.3 The Chay Model;311
13.11;Appendix 10.4 The Fast-Spiking (FS) Model;312
13.12;References;313
14;Delayed RandomWalks: Investigating the Interplay Between Delay and Noise;314
14.1;11.1 Introduction;314
14.2;11.2 Simple RandomWalk;316
14.3;11.3 RandomWalks on a Quadratic Potential;325
14.4;11.4 Delayed RandomWalks;329
14.5;11.5 Postural Sway;335
14.6;11.6 Concluding Remarks;341
14.7;References;341
15;Index;345