1. Introduction.- 2. Time and Change in Economics.- 2.1 Economic Evolution -- An Introduction.- 2.2 Equilibrium Theories in Economic Analysis.

- 2.3 Dynamic Theories in Economics.- 2.4 Samuelson''s Correspondence Principle and Its Limitations.- 2.5 Instabilities in Economic Analysis.- 3. Mathematical Aspects of Dynamic Systems.

- 3.1 Dynamics and Equilibrium.- 3.2 Classifications of Two-Dimensional Differential Equations.- 3.3 The Principle of Linearized Stability.- 3.4 Lyapunov''s Direct Method.

- 3.5 Structural Stability.- 3.6 Conservative Systems.- 3.7 Bifurcation Theory.- 3.8 Singularity Theory.

- 3.9 Catastrophe Theory.- Appendix: Remarks on Bifurcation Theory.- 4. Multiple Equilibria and Structural Changes in Economic Systems.- 4.1 Catastrophe Theory and Comparative Statics Analysis.- 4.

2 Modeling Regional Dynamics.- 4.3 Some Examples of Structural Changes.- 4.3.1 Business Cycles in the Kaldor Model.- 4.3.

2 Resource Management.- 4.3.3 Dynamic Transportation Modal Choice and Bifurcation.- 4.3.4 Multiple Equilibria in Wilson''s Retail Model.- 4.

4 A Bifurcation Analysis for an Economic Growth Model.- 4.5 Singularity Theory in Economic Analysis.- 4.6 Remarks.- 5. Economic Cycles.- 5.

1 Theories of Economic Cycles.- 5.2 Some Mathematical Results Related to Limit Cycles.- 5.2.1 The Poincaré-Bendixson Theorem and Its Applications to Economics.- 5.2.

2 The Hopf Bifurcation Theorem.- 5.3 The Simplified Keynesian Business Cycle Model.- 5.4 Non-equilibrium in a Disequilibrium Model.- 5.5 Monetary Cycles in the Generalized Tobin Model.- 5.

6 Oscillations in van der Ploeg''s Hybrid Growth Model.- 5.7 Periodic Optimal Employment Policy.- 5.8 Optimal Economic Growth Associated with Endogenous Fluctuations.- 5.9 Remarks on Possible Further Bifurcations from Limit Cycles.- 5.

10 Competitive Business Cycles in an Overlapping Generations Economy -- A Discrete Model.- 6. Economic Chaos in Deterministic Systems.- 6.1 Chaos in Deterministic Systems.- 6.2 Economic Chaos in a Discrete System.- 6.

3 Aperiodic Optimal Economic Growth.- 6.4 Urban Dynamics -- The Lorenz System.- 6.5 Chaos in an International Economic Model.- 6.6 Chaos and Economic Forecasting.- 6.

7 Remarks.- Appendix: Some Criteria for Distinguishing Different Attractors.- A.1 The Lyapunov Exponents for Differential Equations.- A.2 The Lyapunov Exponents for Discrete Maps.- A.3 The Signal, Power Spectrum, Autocorrelation Function and Poincaré Map.

- 7. Stochastic Processes and Economic Evolution.- 7.1 Random Processes and Economic Evolution.- 7.2 Stochastic Processes -- An Introduction.- 7.2.

1 Some Concepts in Probability Theory.- 7.2.2 Stochastic Processes.- 7.3 Birth-Death Processes and the Master Equation.- 7.4 A Non-equilibrium Model of the Schumpeter Clock.

- 7.5 Effects of Noise on the Nonlinear Stochastic Systems Close to Critical Points.- 7.6 Effects of Random Environment on a Two-Dimensional Deterministic System Near Critical Points.- 7.7 Conclusions.- 8. Urban Pattern Formation Process -- Stability, Structural Changes and Chaos.

- 8.1 Continuous Spatial Economics and Description of Urban Pattern Formation.- 8.2 The Implications of Structural Stability in the Two-Dimensional Economy.- 83 Economic Cycles in Puu''s Spatial Multiplier-Accelerator Business Model.- 8.4 Spatial Diffusional Effects as a Stabilizer.- 8.

5 Separation and Coexistence of Residents.- 8.6 Long-Term Traveling-Wave Urban Pattern.- 8.7 Instabilities and Urban Pattern Formation.- Appendix: Structural Changes in Two Pattern Formation Models.- A.1 A Model for Morphogenesis.

- A.2 The Brusselator.- 9. The Haken Slaving Principle and Time Scale in Economic Analysis.- 9.1 The Haken Slaving Principle.- 9.2 The Center Manifold Theorem.

- 9.3 Singular Perturbations.- 9.4 Fast Variable Versus Slow Variable in Economic Analysis.- 9.5 The Time Scale in Economic Analysis.- 9.6 Another Problem -- Understanding a Dynamic Man.

- Appendix: The Slaving Principle for Stochastic Differential Equations.- 10. Implications of Synergetic Economics.- 10.1 Synergetic Economics and Its Relations to Synergetics.- 10.2 Relations to Traditional Dynamic Economics.- 10.

3 Competitive and Planned Economies and Synergetic Economics.- 10.4 Implications for Developed and Developing Economies.- 10.5 Chance and Necessity in Economic Life.- 10.6 Policy Decision in a Chaotic World.- 10.

7 Relations Between Microeconomics and Macroeconomics.- 11. Conclusions and Prospects for Further Research.- References.