On Control of Chaos in the R\"{o}ssler system

In order to control chaos, a deep understanding is required on top of good amounts of mathematical and computational~work: First, the system must be numerically integrated to acquire data in order to construct a Poincare map, this is necessary in order~to construct the iterate maps from which the periodic orbits and fixed points (period-1 orbits). Second, the Jacobian is computed at each fixed point. From the Jacobian the eigenverctors and eigenvalues are obtained in order to identify the stable and unstable manifolds. From this point on, one can apply the necessary control algorithms to achieve the desired, predetermined, and controlled~system dynamics.