A novel polynomial method for taming chaos in a wide class of nonlinear oscillators

A novel polynomial method is presented concerning the inhibition of homoclinic chaos in a wide class of nonlinear systems by means of an additional weak perturbation. From Melnikov analysis, we theoretically find parameter-space regions, associated with the chaos-suppressing perturbation, where chaotic states can be suppressed by transforming the problem in a polynomial form. Using this novel focus, an adapted concept of controllability in a Melnikov sense is defined and analyzed by applying the well-known root locus technique from classical control theory.