Stabilization with target oriented control for higher order difference equations.

For a physical or biological model whose dynamics is described by a higher order difference equation u n + 1 = f ( u n , u n − 1 , … , u n − k + 1 ) , we propose a version of a target oriented control u n + 1 = c T + ( 1 − c ) f ( u n , u n − 1 , … , u n − k + 1 ) , with T ≥ 0 , c ∈ [ 0 , 1 ) . In ecological systems, the method incorporates harvesting and recruitment and for a wide class of f , allows to stabilize (locally or globally) a fixed point of f . If a point which is not a fixed point of f has to be stabilized, the target oriented control is an appropriate method for achieving this goal. As a particular case, we consider pest control applied to pest populations with delayed density-dependence. This corresponds to a proportional feedback method, which includes harvesting only, for higher order equations. [ABSTRACT FROM AUTHOR]