H. Castellini et al., ON A METHOD OF CONTROLLING CHAOS ORIGINATING IN A TORUS T2 DESTRUCTION - ITS APPLICATION TO A CHEMICAL CATALYZED REACTION, Chaos, solitons and fractals, 6, 1995, pp. 59-65
The reaction of oxidation of NADH by the enzyme peroxidase was modeled
by Deng, Olsen & Perram in a 8 stage, 4 variable mechanism. The corre
sponding system of non-linear equations exhibits chaotic behavior orig
inating in the destruction of a torus T2. The control of this chaotic
behavior with the use of Ott, Grebogi & Yorke's (OGY)'s method is not
possible because the variables do not converge to the selected fixed p
oint on Poincare's map. We describe a modification of the OGY's method
with the inclusion of a steepest descent algorithm which permits a fa
st control through the variation of one of the kinetic constants. We i
llustrate the modification with some numerical examples in which the e
volution of the chaotic system is converted to a periodic orbit.