Pathways to Hopf Bifurcations in Dynamic Continuous-Time Optimization Problems

Journal of Optimization Theory and Applications

Volumn 91, Issue 2, 1996, Pages 299-320

  Wirl, F ^a  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

Hopf bifurcation; Limit cycles; Optimal control

Indexed keywords

CONTINUOUS TIME SYSTEMS;

CONTINOUS TIME; CONTINUOUS TIME OPTIMIZATION PROBLEMS; CONTROL STATE; LIMIT-CYCLE; OPTIMAL CONTROL MODEL; OPTIMAL CONTROLS; OPTIMAL TRAJECTORIES; TWO-DIMENSIONAL;

HOPF BIFURCATION;

EID: 0030503816     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02190098     Document Type: Article

References (26)

1. RYDER, H. E. JR., and HEAL, G. M., Optimal Growth with Intertemporally Dependent Preferences, Review of Economic Studies, Vol. 40, pp. 1-31, 1973.
2. BENHABIB, J., and NISHIMURA, K., The Hopf Bifurcation and the Existence and Stability of Closed Orbits in Multi-Sector Models of Economic Growth, Journal of Economic Theory, Vol. 21, pp. 421-444, 1979.
3. BENHABIB, J., and RUSTICHINI, A., Equilibrium Cycling with Small Discounting, Journal of Economic Theory, Vol. 52, pp. 423-432, 1990.
4. CARTIGNY, P., and VENDITTI, A., Turnpike Theory: Some New Results on the Saddle Point Property of Equilibria and on the Existence of Endogenous Cycles, Journal of Economic Dynamics and Control, Vol. 18, pp. 957-974, 1994.
5. WIRL, F., Cyclical Strategies in Two-Dimensional Optimal Control Models: Necessary Conditions and Existence, Annals of Operations Research, Vol. 37, pp. 345-356, 1992.
6. HIRSCH, M., and SMALE, S., Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, New York, New York, 1974.
7. GUCKENHEIMER, J., and HOLMES, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields, Springer, New York, New York, 1983.
8. DOCKNER, E., and FEICHTINGER, G., On the Optimality of Limit Cycles in Dynamic Economic Systems, Journal of Economics, Vol. 52, pp. 31-50, 1990.
9. YOUNG, J. T., Is the Entropy Law Relevant to the Economics of Natural Resource Scarcity? Journal of Environmental Economics and Management, Vol. 21, pp. 167-179, 1991.
10. FEICHTINGER, G., and SORGER, G., Optimal Oscillations in Control Models: How Can Constant Demand Lead to Cyclical Production?, Operations Research Letters, Vol. 5, pp. 277-281, 1986.
11. TORO, M., and ARACIL, J., Qualitative Analysis of System Dynamics Ecological Models, System Dynamics Review, Vol. 4, pp. 56-80, 1988.
12. DOCKNER, E., Local Stability Analysis in Optimal Control Problems with Two State Variables, Optimal Control Theory and Economic Analysis, Edited by G. Feichtinger, North Holland, Amsterdam, Holland, Vol. 2, pp. 89-103, 1985.
13. NISHIMURA, K., and TAKAHASHI, H., Factor Intensity and Hopf Bifurcations, Dynamic Economic Models and Optimal Control, Edited by G. Feichtinger, North Holland, Amsterdam, Holland, pp. 135-162, 1992.
14. STIGLER, G. J., and BECKER, G. S., De Gustibus Non Est Disputandum, American Economic Review, Vol. 67, pp. 76-90, 1977.
15. POPPER, K. R., Die erkenntnistheoretische Position der Evolutionären Erkenntnistheorie, 1994, Alles Leben ist Problemlösen, Edited by Karl R. Popper, Piper, München, Germany, pp. 127-144, 1986.
16. BECKER, S. G., and MURPHY, K. M., A Theory of Rational Addiction, Journal of Political Economy, Vol. 96, pp. 675-700, 1988.
17. DOCKNER, E., and FEICHTINGER, G., Cyclical Consumption Patterns and Rational Addiction, American Economic Review, Vol. 83, pp. 256-263, 1993.
18. FEICHTINGER, G., NOVAK, A., and WIRL, F., Limit Cycles in Intertemporal Adjustment Models - Theory and Applications, Journal of Economic Dynamics and Control, Vol. 18, pp. 353-380, 1994.
19. WIRL, F., Complex Dynamic Environmental Policies, Paper Presented at the 6th Annual Congress, European Economic Association, Cambridge, England, 1991.
20. HARTL, R. F., MEHLMANN, A., and NOVAK, A., Periodic Bloodsucking Rates for Vampires, Journal of Optimization Theory and Applications, Vol. 75, pp. 559-568, 1992.
21. WIRL, F., The Ramsey Model Revisited: The Optimality of Cyclical Consumption and Growth, Journal of Economics, Vol. 60, pp. 81-98, 1994.
22. BROCK, W., Money and Growth: The Case of Long-Run Perfect Foresight, International Economic Review, Vol. 15, pp. 750-777, 1974.
23. KONARD, K. A., Wealth Seeking Reconsidered, Journal of Economic Behavior and Organization, Vol. 18, pp. 217-227, 1992.
24. KHIBNIK, A. I., KUZNETSOV, Yu. A., LEVITIN, V. V., and NIKOLAEV, E. V., Interactive Local Bifurcation Analyzer (Manual), Expertise Centre for Computer Algebra in the Netherlands, Amsterdam, Holland, 1992.
25. BROCK, W. A., Pathways to Randomness in the Economy: Emergent Nonlinearity and Chaos in Economics and Finance, Working Paper 93-02-006, Santa Fe Institute, 1993.
26. WIRL, F., and FEICHTINGER, G., Persistent Cyclical Consumption: Variations on the Becker-Murphy Model on Addiction, Rationality and Society, Vol. 7, pp. 149-159, 1995.