Bifurcation and chaos analysis of atomic force microscope system

Atomic force microscope (AFM) is a very high-resolution type of scanning probe microscope, which is an essential characterization and actuation tool in modern nanoscience or engineering. This paper investigates the bifurcation and chaos behavior of the probe tip from AFM system by the differential transformation method (DTM). The dynamic behavior of the probe tip is characterized by reference to bifurcation diagrams, phase portraits, power spectra, Poincar, maps and maximum Lyapunov exponent plots produced using the time-series data obtained from DTM. The results indicate that the probe tip behavior is significantly dependent on the magnitude of the vibrational amplitude. Specifically, the probe tip motion changes from T-periodic to 3T-periodic, then from 2T-periodic to multi-periodic, and finally to chaotic motion with windows of periodic motion as the vibrational amplitude is increased from 0 to 2.0. Furthermore, it is demonstrated that the DTM is in good agreement for the considered system.