Analytical control of homoclinic bifurcation of the hilltop saddle in a noncontact atomic force microcantilever

A control procedure of global dynamics is applied to a reduced order model of noncontact AFM with the aim to shift the homoclinic bifurcation involving the system hilltop saddle. The method consists of adding to the system harmonic excitation controlling superharmonics to be properly identified by solving an optimization problem. The analytical bifurcation threshold is determined through the asymptotic Melnikov method, for the reference system and for the controlled system. The practical effect of the control as regards possibly increasing the system overall robustness by shifting the start of the erosion of the safe basin is then numerically investigated by means of a dynamical integrity analysis based on the evolution of basins of attraction.