Chaos control in the nonlinear Schrödinger equation with Kerr law nonlinearity

Abstract

The nonlinear Schrödinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the distortion in the process of information transmission. We find that fiber-optic transmit signals still present chaotic phenomena if the control intensity is smaller. With the increase of intensity, the fiber-optic signal can stay in a stable state in some regions. When the strength is suppressed to a certain value, an unstable phenomenon of the fiber-optic signal occurs. Moreover we discuss the sensitivities of the parameters to be controlled. The results show that the linear term coefficient and the environment of two quite different frequences have less effects on the fiber-optic transmission. Meanwhile the phenomena of vibration, attenuation and escape occur in some regions.

A hybrid strategy to control uncertain nonlinear chaotic system

“…[2] Chaotic phenomenon is not expected to exist in majority of systems, especially power grid and electronic circuit etc. [3] The efficient control of chaos in chaotic systems has been an attractive research area for few decades.…”