Melnikov’s Criteria and Chaos Analysis in the Nonlinear Schrödinger Equation with Kerr Law Nonlinearity
Joint Authors
Yin, Jiuli
Tian, Lixin
Zhao, Liuwei
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-06-10
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
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 d 1 , and frequency ω 2 of external forcing which can be considered a control strategy, and when the frequenciesy ω 2 and ω 1 approach the maximum frequency of disturbance, the system turmoil intensifies and control intensity increases.
American Psychological Association (APA)
Yin, Jiuli& Zhao, Liuwei& Tian, Lixin. 2014. Melnikov’s Criteria and Chaos Analysis in the Nonlinear Schrödinger Equation with Kerr Law Nonlinearity. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-1033914
Modern Language Association (MLA)
Yin, Jiuli…[et al.]. Melnikov’s Criteria and Chaos Analysis in the Nonlinear Schrödinger Equation with Kerr Law Nonlinearity. Abstract and Applied Analysis No. 2014 (2014), pp.1-12.
https://search.emarefa.net/detail/BIM-1033914
American Medical Association (AMA)
Yin, Jiuli& Zhao, Liuwei& Tian, Lixin. Melnikov’s Criteria and Chaos Analysis in the Nonlinear Schrödinger Equation with Kerr Law Nonlinearity. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-1033914
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1033914