Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems

In this paper, the chaotic behaviors of a nonlinear damped Mathieu system and of a nonlinear nano resonator system with integral orders and with fractional orders are studied. By applying numerical analyses such as phase portraits, Poincaré maps and bifurcation diagrams, the periodic and chaotic motions are observed. It is found that chaos exists both in the nonlinear damped Mathieu system and in the integral order and fractional order nano resonator systems.