On Stability and Bifurcation of Solutions of Nonlinear System of Differential Equations for AIDS Disease | Science Publications

S. A.A. El-Marouf

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On Stability and Bifurcation of Solutions of Nonlinear System of Differential Equations for AIDS Disease | Science Publications

机译：艾滋病疾病微分方程非线性系统解的稳定性和分歧科学出版物

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> Problem statement: This study aims to discuss the stability and bifurcation of a system of ordinary differential equations expressing a general nonlinear model of HIV/AIDS which has great interests from scientists and researchers on mathematics, biology, medicine and education. The existance of equilibrium points and their local stability are studied for HIV/AIDS model with two forms of the incidence rates. Conclusion/Recommendations: A comparison with recent published results is given. Hopf bifurcation of solutions of an epidemic model with a general nonlinear incidence rate is established. It is also proved that the system undergoes a series of Bogdanov-Takens bifurcation, i.e., saddle-node bifurcation, Hopf bifurcation and homoclinic bifurcation for suitable values of the parameters.

机译： > 问题陈述：该研究旨在讨论表达HIV / AIDS通用非线性模型的常微分方程组的稳定性和分歧，这引起了科学家和研究人员的极大兴趣关于数学，生物学，医学和教育。针对艾滋病毒/艾滋病模型，以两种形式的发病率研究了平衡点的存在及其局部稳定性。结论/建议：与最近发表的结果进行了比较。建立了具有一般非线性发生率的流行病模型解的Hopf分支。还证明了该系统经历一系列Bogdanov-Takens分叉，即，对于参数的合适值，鞍形节点分叉，Hopf分叉和同斜分叉。

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《American journal of applied sciences》 |2012年第7期|共页
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S. A.A. El-Marouf;
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中图分类自然科学研究方法;
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1. On Stability and Bifurcation of Solutions of Nonlinear System of Differential Equations for AIDS Disease [J] . El-Marouf S.A.A. American journal of applied sciences . 2012,第7期

机译：艾滋病疾病非线性微分方程组解的稳定性与分支。
2. A frequency-domain approach to the analysis of stability and bifurcations in nonlinear systems described by differential-algebraic equations [J] . F. L. Traversa, F. Bonani, S. Donati Guerrieri International journal of circuit theory and applications . 2008,第4期

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3. Approximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform Method | Science Publications [J] . Asad Freihat, Eman Abuteen, Hammad Khalil, Journal of Mathematics and Statistics . 2016,第1期

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4. Application of Admissible Functions in Studying Partial Stability of Solutions of a Nonlinear System of Differential Equations [C] . M.Yu. Filimonov International Conference on Applications of Mathematics in Engineering and Economics . 2018

机译：可允许功能在差分方程的非线性系统溶液局部稳定性中的应用
5. Symmetric systems of implicit functional differential equations: Existence of solutions and bifurcation results. [D] . Li, Zhichao. 2013

机译：隐式泛函微分方程的对称系统：解和分支结果的存在。
6. Stability and square integrability of derivatives of solutions of nonlinear fourth order differential equations with delay [O] . Erdal Korkmaz -1

机译：时滞非线性四阶微分方程解的导数的稳定性和平方可积性。
7. On Stability and Bifurcation of Solutions of Nonlinear System of Differential Equations for AIDS Disease [O] . S. A.A. El-Marouf 2012

机译：艾滋病疾病非线性微分方程组解的稳定性与分支。
8. Bifurcation and Stability for a Nonlinear Parabolic Partial Differential Equation [R] . Chafee, N. 1973

机译：非线性抛物型偏微分方程的分支与稳定性

On Stability and Bifurcation of Solutions of Nonlinear System of Differential Equations for AIDS Disease | Science Publications

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