Genesis of indifference thresholds in discrete time optimal control problems: with applications to the lake pollution problem
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چکیده
This article investigates the indifference-attractor bifurcation of infinite horizon discrete-time optimal control problems with a single state variable. We show that these bifurcations are linked to a heteroclinic bifurcation scenario of the statecostate equations, and we analyse the consequences for the optimal solutions. In particular, we can characterise the bifurcation value at which indifference thresholds appear by a geometric condition, and we find that for certain parameter values, there are countably infinitely many indifference points. We apply our results to a modified version of the lake pollution management problem.
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