Chaos suppression in flows using proportional praises in the system variables

In this work a detailed analysis of a recently introduced chaos suppression method through proportional perturbations in the system variables [M.A. Matias and J. Guemez, Phys. Rev. Lett. 72, 1455 (1994)] is presented. The method does not require any previous knowledge of the system dynamics and could be specially useful for those systems, e.g., chemical or biological, for which it may be advantageous to act on the system variables rather than on the parameters. The performance of the method is illustrated with several autonomous and nonautonomous flows, including issues such as the possibility of stabilizing different periodic of fixed point behaviors. Finally, a quantitative relationship among the parameters of the method is sought in terms of the highest Lyapunov exponent of the system.