Taming Chaotic Solitons in Frenkel-Kontorova Chains by Weak Periodic Excitations

Abstract

We have proposed theoretically and confirmed numerically the possibility of controlling chaotic solitons in damped, driven Frenkel-Kontorova chains subjected to additive bounded noise by weak periodic excitations. Theoretically, we obtained an effective equation of motion governing the dynamics of the soliton center of mass for which we deduced Melnikov’s method-based predictions concerning the regions in the control parameter space where homoclinic bifurcations are frustrated. Numerically, we found that such theoretical predictions can be reliably applied to the original Frenkel-Kontorova chains, even for the case of localized application of the soliton-taming excitations, and there is strikingly good agreement between analytical estimates and numerical results.