Modeling and Computations in Dynamical S: Dedicated to John Von Neumann

CONTENTS......Page 6
Editorial
......Page 8
Transport in Dynamical Astronomy and Multibody Problems......Page 10
1. Introduction......Page 11
2. Description of the PCR3BP Global Dynamics......Page 15
3. Computing Transport......Page 17
4. Example: The Sun-Jupiter-Asteroid System......Page 26
5. Conclusions and Future Directions......Page 34
1. Introduction......Page 40
2. Discretization as a Family of Approximating Discrete-Time Semidynamical Systems......Page 41
3. Qualitative Numerics for Delay Equations......Page 48
4. Remarks on Functional Differential Equations......Page 52
1. Introduction......Page 54
2. Autonomous Systems......Page 55
3. Nonautonomous Systems......Page 59
4. A Total Stability Theorem......Page 64
5. Applications of the Total Stability Theorem......Page 66
6. Concluding Remarks and Questions......Page 67
A. Appendix: Proof of Theorem 1......Page 69
1. Introduction......Page 74
2. Approximation by Geodesic Level Sets......Page 79
3. BVP Continuation of Trajectories......Page 82
4. Computation of Fat Trajectories......Page 87
5. PDE Formulation......Page 90
6. Box Covering......Page 95
7. Discussion......Page 98
1. Norms and Commutators in Mn[R] and sO(n)......Page 104
2. The Reduced Commutator Matrix in so(n)......Page 106
3. The Radius of so(n) for n > 4......Page 110
4. Conclusion......Page 112
1. Introduction......Page 114
2. Models of Decision Tasks......Page 116
3. Optimal Signal Discrimination in the One-Dimensional Models......Page 126
4. The Locus Coeruleus Brainstem Area and Optimal Gain Trajectories......Page 133
5. Discussion and Conclusions......Page 135
1. Introduction......Page 138
2. The Central Path is a Trajectory of the Newton Vector Field......Page 139
3. An Analytic Expression for the Newton Vector Field......Page 141
4. Extension to the Faces of p......Page 143
5. Analyticity and Derivatives......Page 147
6. Example......Page 149
1. Introduction......Page 152
2. Equilibria and their Branch Points......Page 153
3. Periodic Solutions and their Branch Points......Page 155
4. Numerical Detection Computation and Continuation of Branch Points of Periodic Solutions......Page 157
5. Example 1: The A -> B -> C Reaction......Page 161
6. Example 2: An Electronic Circuit......Page 166
1. Introduction......Page 172
2. Definitions and Assumptions......Page 173
3. The Main Result: The Conditions for Am =BMN......Page 175
4. Application of the Coarse-Grained Model......Page 177
5. Summary and Related Topics......Page 180
1. Introduction......Page 182
2. Analysis......Page 184
3. Global Computations and their Interpretation......Page 191
4. Summary and Related Issues......Page 200
1. Introduction......Page 202
2. Example......Page 203
3. Generic Codimension-One Bifurcations of Stable Sets......Page 206
4. Bifurcations of Basin Boundaries......Page 210
5. Stable Set versus Unstable Manifold......Page 211
6. Conclusions......Page 214
1. Introduction......Page 216
2. Codimension-One and -Two Bifurcations of Equilibria......Page 218
3. Degenerate Bogdanov-Takens Bifurcations......Page 225
4. Homoclinic Orbits and Their Numerical Continuation......Page 229
5. Homoclinic Bifurcations in the Enzyme System......Page 235
6. Bifurcation Sets......Page 247
7. Conclusions......Page 255
1. Introduction......Page 260
2. Formulation......Page 262
3. Numerical Implementation......Page 263
4. Examples......Page 265
5. Concluding Remarks......Page 275
1. Background and Basic Result......Page 278
3. Examples......Page 283
1. Introduction......Page 286
2. A Coarse Time Stepper for Discrete Systems......Page 287
3. A Discrete Traveling Front Example......Page 290
4. Numerical Results......Page 295
5. An Alternative Continuum Approach: Pade Approximations......Page 301
6. Summary and Discussion......Page 304
1. Introduction......Page 308
2. Background on Model Reduction......Page 309
3. Balanced POD......Page 313
4. Example: Linearized Channel Flow......Page 316
5. Conclusions......Page 322
Appendix A Theorems on Computing Balancing Transformations......Page 323
1. Introduction......Page 326
2. Bifurcation Tracking Algorithms......Page 328
3. Bifurcation Analysis of Rayleigh-Benard Convection in a 5 x 5 x 1 Box......Page 333
4. Summary and Conclusions......Page 341
1. Introduction and Preliminary Definitions......Page 344
2. The Problem of Invariant Algebraic Curves from the Point of View of Linear Algebra......Page 347
3. The Algorithm......Page 348
4. Examples......Page 349
Author Index......Page 356