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

Chen Xianwei; Yuan Shaoliang; Jing Zhujun; Fu Xiangling

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

机译：组织炎症离散数学模型的分叉与混沌

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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.

机译：在本文中，详细研究了由欧拉获得的组织炎症的离散时间数学模型。利用中心流形定理和分叉理论推导了折叠分叉，翻转分叉和霍普夫分叉的存在条件，并通过分析方法证明了马洛托意义上的混沌。绘制了包括分叉图，李雅普诺夫指数，分形维数和相像在内的数值模拟，以完美显示与理论分析的一致性。

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来源
《Journal of dynamics and differential equations》 |2016年第1期|281-299|共19页
作者
Chen Xianwei; Yuan Shaoliang; Jing Zhujun; Fu Xiangling;
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作者单位

Hunan Univ Sci & Technol, Sch Math & Computat Sci, Xiangtan 411201, Peoples R China;

Yichun Univ, Coll Math & Comp Sci, Yichun 336000, Jiangxi, Peoples R China;

Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China;

Hunan Univ Sci & Technol, Sch Math & Computat Sci, Xiangtan 411201, Peoples R China;

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正文语种 eng
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关键词
Tissue inflammation; Fold bifurcation; Flip bifurcation; Hopf bifurcation; Marotto's chaos;

机译：组织炎症;折叠分叉;翻转分叉;霍普夫分叉;马洛托的混乱;

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

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