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.- 4.4 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.- 5.3 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.- 6.5Chaos in an International Economic Model.- 6.6 Chaos and Economic Forecasting.- 6.7 Remarks.- Appendix: Some Criteria for Distinguishing Different Attractors.- 7. Stochastic Processes and Economic Evolution.- 7.1 Random Processes and Economic Evolution.- 7.2 Stochastic Processes — An Introduction.- 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.- 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.- 10.4Implications 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.