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Abstract and Applied Analysis
Volume 2014, Article ID 650781, 12 pages
Research Article

Melnikov’s Criteria and Chaos Analysis in the Nonlinear Schrödinger Equation with Kerr Law Nonlinearity

Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China

Received 27 January 2014; Accepted 30 April 2014; Published 10 June 2014

Academic Editor: Guanglu Zhou

Copyright © 2014 Jiuli Yin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 controller e, amplitude , and frequency of external forcing which can be considered a control strategy, and when the frequenciesy and approach the maximum frequency of disturbance, the system turmoil intensifies and control intensity increases.