Abstract
The dynamics of the nonlinear Schrödinger equation with Kerr law nonlinearity with two perturbation terms are investigated. By using Melnikov method, the threshold values of chaotic motion under periodic perturbation are given. Moreover we also study the effects of the parameters of system on dynamical behaviors by using numerical simulation. The numerical simulations, including bifurcation diagram of fixed points, chaos threshold diagram of system in three-dimensional space, maximum Lyapunov exponent, and phase portraits, are also plotted to illustrate theoretical analysis and to expose the complex dynamical behaviors. In particular, we observe that the system can leave chaotic region to periodic motion by adjusting controllere, amplituded1, and frequencyω2of external forcing which can be considered a control strategy, and when the frequenciesyω2andω1approach the maximum frequency of disturbance, the system turmoil intensifies and control intensity increases.
Highlights
Fiber-optic signal transmission has a very wide application in the real life, which makes our lives more convenient and quicker
We study the bifurcation and dynamical behaviors depending on the parameters by using bifurcation and chaos theories in [15– 21] and numerical simulation
(ii) We study the effects of the parameters of system on dynamical behaviors by using numerical simulation
Summary
Fiber-optic signal transmission has a very wide application in the real life, which makes our lives more convenient and quicker. Fiber-optic signals make it seem that the signal propagation cannot exist in pure environment It is always influenced by external environmental perturbations. One of the famous fiber-optic models is the external periodic perturbations of the nonlinear Schrodinger equation with Kerr law nonlinearity [6]. Equation (1) describes the propagation of optical solitons in nonlinear optical fibers that exhibits a Kerr law nonlinearity. The study of perturbed nonlinear Schrodinger’s equation with Kerr law nonlinearity is of fundamental and even practical interest. Eminent characteristics of perturbed nonlinear Schrodinger’s equation with Kerr law nonlinearity have a rich content of nonlinear properties which are suitable for a detailed investigating of various dynamical states. The numerical simulations, including bifurcation diagram of fixed points, chaos threshold diagram of system in three-dimensional space, maximum Lyapunov exponent, and phase portraits, are plotted to illustrate theoretical analysis and to expose the complex dynamical behaviors.
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