Controlling Chaos in Porous Media Convection by Using Feedback Control

A method of using feedback control to promote or suppress the transition to chaos in porous media convection is demonstrated in this article. A feedback control suggested by Mahmud and Hashim (Transp Porous Media, doi:10.1007/s11242-009-9511-1, 2010) is used in the present article to provide a comparison between an analytical expression for the transition point to chaos and numerical results. In addition, it is shown that such a feedback control can be applied as an excellent practical means for controlling (suppressing or promoting) chaos by using a transformation made by Magyari (Transp Porous Media, doi:10.1007/s11242-009-9511-1, 2010). The latter shows that Mahmud and Hashim (Transp Porous Media, doi:10.1007/s11242-009-9511-1, 2010) model can be transformed into Vadasz-Olek's model (Transp Porous Media 37(1):69-91, 1999a) through a simple transformation of variables implying that the main effect the feedback control has on the solution is equivalent to altering the initial conditions. The theoretical and practical significance of such an equivalent alteration of the initial conditions is presented and discussed.