Control of Homoclinic Chaos by Weak Periodic Perturbations

This monograph presents a reasonably rigorous theory of a highly relevant chaos control method: suppression-enhancement of chaos by weak periodic excitations in low-dimensional, dissipative and non-autonomous systems. The theory provides analytical estimates of the ranges of parameters of the chaos-controlling excitation for suppression-enhancement of the initial chaos. The important applications of the theory presented in the text include: control of chaotic escape from a potential well; suppression of chaos in a driven Josephson junction; and control of chaotic solitons in Frenkel-Kontorova chains.