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Synchronization dependence on initial setting of chaotic systems without equilibria

Author

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  • Wu, Fuqiang
  • Zhou, Ping
  • Alsaedi, Ahmed
  • Hayat, Tasawar
  • Ma, Jun

Abstract

An initial-dependent system is developed from an electromotor driven by nonlinear torque. Standard nonlinear analysis is carried out and chaotic region is explored in the dynamical system without equilibria. Phase portrait, Lyapunov exponent spectrum, Hamilton energy and bifurcation analysis are calculated to confirm the emergence of chaos and state selection. It is found that the attractor type (periodical or chaotic) is dependent on the initial setting. Furthermore, bidirectional coupling is used to detect the synchronization approach between two initial-dependent electomotors. In the case of network synchronization and pattern selection, a chain network is designed and statistical factor of synchronization is calculated to predict the synchronization stability on the network. It is found that the synchronization stability shows some dependence on initial setting for one variable(external load). The Hamilton energy is also calculated to find the behavior dependence on initial setting and parameter selection by using Helmholtz theorem.

Suggested Citation

  • Wu, Fuqiang & Zhou, Ping & Alsaedi, Ahmed & Hayat, Tasawar & Ma, Jun, 2018. "Synchronization dependence on initial setting of chaotic systems without equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 124-132.
    • Handle: RePEc:eee:chsofr:v:110:y:2018:i:c:p:124-132
    DOI: 10.1016/j.chaos.2018.03.024
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    1. Su, Lei & Shen, Hao, 2015. "Mixed H∞/passive synchronization for complex dynamical networks with sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 931-942.
    2. Wu, Fuqiang & Wang, Chunni & Jin, Wuyin & Ma, Jun, 2017. "Dynamical responses in a new neuron model subjected to electromagnetic induction and phase noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 81-88.
    3. Ma, Jun & Wu, Fuqiang & Ren, Guodong & Tang, Jun, 2017. "A class of initials-dependent dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 65-76.
    4. Muhammad Iqbal & Muhammad Rehan & Keum-Shik Hong, 2017. "Modeling of inter-neuronal coupling medium and its impact on neuronal synchronization," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-20, May.
    5. Dmitri B. Strukov & Gregory S. Snider & Duncan R. Stewart & R. Stanley Williams, 2008. "The missing memristor found," Nature, Nature, vol. 453(7191), pages 80-83, May.
    6. Wu, Fuqiang & Wang, Ya & Ma, Jun & Jin, Wuyin & Hobiny, Aatef, 2018. "Multi-channels coupling-induced pattern transition in a tri-layer neuronal network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 54-68.
    7. Cang, Shijian & Wu, Aiguo & Wang, Zenghui & Chen, Zengqiang, 2017. "On a 3-D generalized Hamiltonian model with conservative and dissipative chaotic flows," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 45-51.
    8. Lulu Lu & Ya Jia & Wangheng Liu & Lijian Yang, 2017. "Mixed Stimulus-Induced Mode Selection in Neural Activity Driven by High and Low Frequency Current under Electromagnetic Radiation," Complexity, Hindawi, vol. 2017, pages 1-11, October.
    9. Jafari, Sajad & Sprott, J.C., 2013. "Simple chaotic flows with a line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 79-84.
    10. El-Gohary, Awad & Sarhan, Ammar, 2006. "Optimal control and synchronization of Lorenz system with complete unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1122-1132.
    11. Ma, Jun & Mi, Lv & Zhou, Ping & Xu, Ying & Hayat, Tasawar, 2017. "Phase synchronization between two neurons induced by coupling of electromagnetic field," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 321-328.
    12. Zhang, Ge & Ma, Jun & Alsaedi, Ahmed & Ahmad, Bashir & Alzahrani, Faris, 2018. "Dynamical behavior and application in Josephson Junction coupled by memristor," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 290-299.
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