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The present value of resources with large discount rates. (English) Zbl 0881.49002
The authors have described a method to detect limit cycles for optimal control problems in the plane. This method has been applied to two specific examples from resource management: a taxation problem and an exploited system of predator-prey interaction which show that the limit cycles may grow as the discount rates decrease. The relation of the established results to theorems in optimal growth theory has also been discussed.

49J15 Existence theories for optimal control problems involving ordinary differential equations
92D25 Population dynamics (general)
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
Full Text: DOI
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