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Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation

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Abstract

In this paper, the discrete-time mathematical model for tissue inflammation obtained by Euler is investigated in detail. Conditions of the existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, and chaos in the sense of Marotto is proved by analytical method. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, fractal dimensions, and phase portraits are plotted to perfectly show the consistence with the theoretical analysis.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (No. 11361067).

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, 411201, People’s Republic of China

    Xianwei Chen & Xiangling Fu

  2. College of Mathematics and Computer Sciences, Yichun University, Yichun, 336000, Jiangxi, People’s Republic of China

    Shaoliang Yuan

  3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Zhujun Jing

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  1. Xianwei Chen
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  2. Shaoliang Yuan
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  3. Zhujun Jing
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  4. Xiangling Fu
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Correspondence to Xianwei Chen.

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Chen, X., Yuan, S., Jing, Z. et al. Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation. J Dyn Diff Equat 28, 281–299 (2016). https://doi.org/10.1007/s10884-014-9413-y

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  • DOI: https://doi.org/10.1007/s10884-014-9413-y

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