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Qualitative and quantitative analysis of nonlinear dynamics by the complete discrimination system for polynomial method

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  • Kai, Yue
  • Chen, Shuangqing
  • Zheng, Bailin
  • Zhang, Kai
  • Yang, Nan
  • Xu, Wenlong

Abstract

We show that via the complete discrimination system for polynomial method, the bifurcation, critical condition and topological properties of the nonlinear dynamics can be seen very easily. Concrete example of perturbed Gardner’s equation with high order dispersion also verifies our conclusion. The results indicate that the complete discrimination system for polynomial method can not only be used to get quantitative results such as the classification of the traveling wave solutions, but also to conduct qualitative analysis for the nonlinear differential equations.

Suggested Citation

  • Kai, Yue & Chen, Shuangqing & Zheng, Bailin & Zhang, Kai & Yang, Nan & Xu, Wenlong, 2020. "Qualitative and quantitative analysis of nonlinear dynamics by the complete discrimination system for polynomial method," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307104
    DOI: 10.1016/j.chaos.2020.110314
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    References listed on IDEAS

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    1. Cemil Tunç & Sultan Erdur, 2018. "New Qualitative Results for Solutions of Functional Differential Equations of Second Order," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-13, October.
    2. Li, Li & Wang, Zhen & Li, Yuxia & Shen, Hao & Lu, Junwei, 2018. "Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 152-169.
    3. Liu, Cheng-shi, 2009. "Exponential function rational expansion method for nonlinear differential–difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 708-716.
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    Cited by:

    1. Kai, Yue & Li, Yaxi & Huang, Liuke, 2022. "Topological properties and wave structures of Gilson–Pickering equation," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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