Chaotic control has to deal with correlation dimension, entropy values, topology and other strange attractor´s characteristics

Research on the control of chaotic dynamics seeks in general to make a strange attractor (SA) disappear, in order to replace it by a quasi periodic attractor (QPA), and less often to change a QPA in a low dimensional SA. However, our biological experience incited us to choose other control goals. First, a determination of the controlled strange attractor correlation dimension seemed to be necessary, just as system entropy, if normal values were known, or yet other SA characteristics-given that normal functioning of a lot of biological systems seems to be better when low-dimensional chaotic dynamics are present. We were also engaged in controlling an abnormal topology of the SA (its place in the space phase), given that the mean of the trajectories values had to be taken into account, according to the ergodic hypothesis. We report some simulations based on the so-called `model for the regulation of agonistic antagonistic couples´-which includes several couples of endogenous state variables and here only one couple of exogenous control variables-to point out a theoretical outline of these problems