Genesis of indifference thresholds and infinitely many indifference points in discrete time infinite horizon optimisation problems

This article investigates the discrete time analogon of the indifference-attractor bifurcation of infinite horizon continuous-time optimal control problems with a single state variable. We show that these bifurcations are linked to a heteroclinic bifurcation scenario of the state-costate 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 shallow lake pollution management problem.