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Dynamic Analysis for a Fractional‐Order Autonomous Chaotic System

Author

Listed:
  • Jiangang Zhang
  • Juan Nan
  • Wenju Du
  • Yandong Chu
  • Hongwei Luo

Abstract

We introduce a discretization process to discretize a modified fractional‐order optically injected semiconductor lasers model and investigate its dynamical behaviors. More precisely, a sufficient condition for the existence and uniqueness of the solution is obtained, and the necessary and sufficient conditions of stability of the discrete system are investigated. The results show that the system’s fractional parameter has an effect on the stability of the discrete system, and the system has rich dynamic characteristics such as Hopf bifurcation, attractor crisis, and chaotic attractors.

Suggested Citation

  • Jiangang Zhang & Juan Nan & Wenju Du & Yandong Chu & Hongwei Luo, 2016. "Dynamic Analysis for a Fractional‐Order Autonomous Chaotic System," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:8712496
    DOI: 10.1155/2016/8712496
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    References listed on IDEAS

    as
    1. Shaher Momani & Asad Freihat & Mohammed AL-Smadi, 2014. "Analytical Study of Fractional‐Order Multiple Chaotic FitzHugh‐Nagumo Neurons Model Using Multistep Generalized Differential Transform Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Shaher Momani & Asad Freihat & Mohammed AL-Smadi, 2014. "Analytical Study of Fractional-Order Multiple Chaotic FitzHugh-Nagumo Neurons Model Using Multistep Generalized Differential Transform Method," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, June.
    3. Li, Xiaofeng & Pan, Wei & Luo, Bin & Ma, Dong & Wang, Yong & Li, Nuohan, 2006. "Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1387-1394.
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