On a method of controlling chaos originating in a torus t2 destruction: Its application to a chemical catalyzed reaction

The reaction of oxidation of NADH by the enzyme peroxidase was modeled by Deng, Olsen & Perram in a 8 stage, 4 variable mechanism. The corresponding system of non-linear equations exhibits chaotic behavior originating in the destruction of a torus T2. The control of this chaotic behavior with the use of Ott, Grebogi & Yorkeʹs (OGY)ʹs method is not possible because the variables do not converge to the selected fixed point on Poincareʹs map. We describe a modification of the OGYʹs method with the inclusion of a steepest descent algorithm which permits a fast control through the variation of one of the kinetic constants. We illustrate the modification with some numerical examples in which the evolution of the chaotic system is converted to a periodic orbit.