Maintenance of transient chaos using a neural-network-assisted feedback control.

A stable period-3 orbit in the parametric vicinity of a chaotic attractor is destabilized using two distinct feedback strategies. This results in the inception and subsequent maintenance of the otherwise short-lived chaotic transients. Both the techniques employed are based on the exclusion of trajectories from the near vicinity of the open loop stable period-3 attractor; the first relies on the traditional proportional feedback method while the second one includes a predictive term enabling delimitation of exclusion zones for the system dynamics. The implementation of these strategies involves construction of appropriate reference models in the form of an artificial-neural-network approximator.