Comparative analysis of a heuristic control of chaos algorithm in some model systems

In this work we propose a Heuristic algorithm based on parametric perturbat ion for control of chaos in systems of ODEs. This method appears to be the first to apply a perturbation to a parameter in a system of ODEs that is ac tive over a finite length of time only. The method proposed is comparativel y easy to implement and needs almost no information about the system beyond the existence of a system-wide controllable parameter. We demonstrate cert ain advantages of this technique over two well-known algorithms, namely, co ntrol by periodic parametric perturbation and control by addition of a seco nd weak periodic force, such as the possibility of switching behavior, pret argetting the period of the controlled orbit, stabilizing high period orbit s etc. We also demonstrate the applicability of the technique in certain nu merical models of physical systems and also in a rather difficult model pro blem, viz. the control of the rheological parameters of periodically forced suspensions of slender rods in simple shear flow.