Suppression of chaos through changes in the system variables through Poincare and Lorenz return maps

The present paper introduces a new chaos suppression method that is able to stabilize N-dimensional flows by perturbing the state variables in a discrete way when the flow crosses a suitably chosen Poincare section. Two versions of the method are presented, depending on whether the perturbations are introduced on a proportional or an additive fashion. The perturbations are applied to the corresponding N-1-dimensional Poincare map, or, in the case of strongly dissipative systems, to a suitable one-dimensional Lorenz map. The method is applied to two different three-variable flows: Rossler spiral chaos model and an isothermal three-variable autocatalator model introduced by Peng et al.