Chaos occurs easily in the nonlinear Schr？dinger equation with external perturbations owing to the absence of damping. For the process of information transmission, the perturbation will cause distortion. If we add a suitable controller, it is easy to discover that chaos still appears in the process of propagation of fiber-optic signal when the strength of controller is weak. With the strength of controller increasing, the propagation of fiber-optic signal will arrive at the stable state. As the strength exceeds a certain degree, the propagation of fiber-optic signal system would tend toward the unstable state. Moreover, we consider the parameters’ sensitivity to be controlled. The result demonstrates that the nonlinear term parameter and the two quite different frequencies have less effect on the propagation of fiber-optic signal. Meanwhile, the phenomena of vibration, oscillation, and escape occur in some regions. 1. Introduction The cubic quintic nonlinear Schr？dinger (NLS) equation is extensively used in various fields, especially for the process of the fiber-optic signal propagation [1]. Here represents the nondimensional distance along the fiber-optic signal, represents time in a dimensionless form, and and are real valued constants. The dependent variable function is a complex valued function that represents the signal wave profile. In a general way, (1) is a nonlinear partial differential equation, which is completely integrable on the infinite line or periodic boundary conditions in one dimension. As a matter of fact, the propagation of fiber-optic signal must be perturbed with external environment. Extensive systems with external perturbations have been widely investigated by using analytic methods and numerical simulations. A mass of bifurcation sets, the routes to chaos, and Lyapunov exponents are given in [2–4]. More attention has been paid to the interaction of external perturbations. The analysis of complex dynamics in three-well forcing or other systems with two external forcings are shown in [5–7]. Although these researches have played a certain role in chaos control, there are rarely researches on the fiber-optic signal models with two-frequency perturbations. However, two-frequency perturbations can model the fiber-optic signal under complex external conditions better. Hence, we consider the fiber-optic signal system (1) under two-frequency perturbations where are the amplitudes of the perturbations and are the frequencies; is the velocity of a certain signal. The research purposes of this paper are the two following vital points.
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