Collective escape and homoclinic bifurcation phenomena in a nonlinear oscillators chain

Foudjio, Michael Mekontchou, Ndjomatchoua, Frank Thomas, Gninzanlong, Carlos Lawrence and Tchawoua, Clément. 2022. Collective escape and homoclinic bifurcation phenomena in a nonlinear oscillators chain. Communications in Nonlinear Science and Numerical Simulation 114:106690.

The phenomenon of deterministic collective escape of particles from the cubic on-site potential well in the presence of both uniform damping and a periodic force is studied. Using analytical techniques such as the separation of time and space as well as the Melnikov theorem, the condition on the periodic force for which a single particle exhibits an irregular motion induced by the homoclinic bifurcation (HB) is derived. Numerical simulation showed that this irregular motion can lead to a strong localization of energy on all the coupled particles allowing them to collectively cross the energy barrier. Moreover, the critical value of the driving force inducing collective escape increases as the potential energy barrier increases and decreases as its frequency increases. Depending on the frequency range of the driving frequency, the collective escape and HB can occur simultaneously; otherwise, the HB prevails.