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Preface | ||
Acknowledgments | ||
Pt. I | Theory | |
1 | Preliminaries | 3 |
2 | Dynamics on the Real Line | 13 |
1 | Equilibria and their Stability | 13 |
2 | Cycles and Limit Cycles | 33 |
3 | Elementary Bifurcations | 51 |
3 | Vector Difference Equations | 71 |
1 | Stability | 71 |
2 | Semiconjugates of maps of the line | 79 |
3 | Chaotic Maps | 112 |
4 | Polymodal systems and thresholds | 140 |
4 | Higher Order Scalar Difference Equations | 165 |
1 | Boundedness and persistent oscillations | 165 |
2 | Permanence | 185 |
3 | Global attractivity and related results | 200 |
Pt. II | Applications to Social Science Models | |
5 | Chaos and Stability in Some Models | 243 |
1 | The Accelerator-Multiplier Business Cycle Models | 243 |
2 | A productivity growth model | 269 |
3 | Chaos and competition in a model of consumer behavior | 274 |
4 | An overlapping generations consumption-loan model | 287 |
5 | A dynamical model of consumer demand | 291 |
6 | A bimodal model of combat | 310 |
6 | Additional Models | 339 |
1 | Addiction and habit formation | 339 |
2 | Budgetary competition | 341 |
3 | Cournot duopoly | 343 |
4 | Chaos in real exchange rates | 345 |
5 | Real wages and mode switching | 346 |
6 | Chaos in a dynamic equilibrium model | 349 |
7 | Oscillatory behavior in an OLG model | 352 |
8 | Attractor basins and critical curves in two models | 353 |
9 | Reducing inflation: Gradual vs. shock treatments | 355 |
10 | Walrasian tatonnement with adaptive expectations | 358 |
11 | Socio-spatial dynamics | 361 |
12 | Models of arms race | 363 |
Bibliography | 367 | |
Index | 385 |
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