Effective suppressibility of chaos.

Suppression of chaos is a relevant phenomenon that can take place in nonlinear dynamical systems when a parameter is varied. Here, we investigate the possibilities of effectively suppressing the chaotic motion of a dynamical system by a specific time independent variation of a parameter of our system. In realistic situations, we need to be very careful with the experimental conditions and the accuracy of the parameter measurements. We define the suppressibility, a new measure taking values in the parameter space, that allows us to detect which chaotic motions can be suppressed, what possible new choices of the parameter guarantee their suppression, and how small the parameter variations from the initial chaotic state to the final periodic one are. We apply this measure to a Duffing oscillator and a system consisting on ten globally coupled Hénon maps. We offer as our main result tool sets that can be used as guides to suppress chaotic dynamics.