Comparative Analysis of a Heuristic Control of Chaos Algorithm in some Model Systems

In this work we propose a Heuristic algorithm based on parametric perturbation 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 active over a finite length of time only. The method proposed is comparatively easy to implement and needs almost no information about the system beyond the existence of a system-wide controllable parameter. We demonstrate certain advantages of this technique over two well-known algorithms, namely, control by periodic parametric perturbation and control by addition of a second weak periodic force, such as the possibility of switching behavior, pretargetting the period of the controlled orbit, stabilizing high period orbits etc. We also demonstrate the applicability of the technique in certain numerical models of physical systems and also in a rather difficult model problem, viz. the control of the rheological parameters of periodically forced suspensions of slender rods in simple shear flow.