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For a physical or biological model whose dynamics is described by a higherorder difference equation $u_{n+1}=f(u_n,u_{n-1}, \dots, u_{n-k+1})$, wepropose a version of a target oriented control $u_{n+1}=cT+(1-c)f(u_n,u_{n-1},\dots, u_{n-k+1})$, with $T\ge 0$, $c\in [0,1)$. In ecological systems, themethod incorporates harvesting and recruitment and for a wide class of $f$,allows to stabilize (locally or globally) a fixed point of $f$. If a pointwhich is not a fixed point of $f$ has to be stabilized, the target orientedcontrol is an appropriate method for achieving this goal. As a particular case,we consider pest control applied to pest populations with delayeddensity-dependence. This corresponds to a proportional feedback method, whichincludes harvesting only, for higher order equations.

Stabilization with target oriented control for higher order difference equations