A novel adaptive procedure for stabilising certain types of non-linear, time-varying, discrete system is described. Its application to one-dimensional unimodal systems, which are particularly important in the dynamic modelling of biological populations, is illustrated. An unusual feature is that the controlled system automatically locates a natural equilibrium state, as opposed to being driven to a pre-defined set point. This has the important advantage in the control of biological populations of minimal interference with the system. Robust equilibrium is maintained, not only in the period-doubling and chaos regions, but also deep into the catastrophically unstable extinction region.
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