Bifurcation theory, computation and applications
分岔理论、计算与应用
基本信息
- 批准号:RGPIN-2015-06210
- 负责人:
- 金额:$ 1.46万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2017
- 资助国家:加拿大
- 起止时间:2017-01-01 至 2018-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Many problems arising in science and engineering can be modelled by mathematical systems that dynamically evolve in time. Among them, nonlinear differential equations are widely used to describe complex phenomena, such as vibration of machinery, weather patter, animal locomotion, population growth, financial markets, spread of diseases, recurrent infection, etc. Such dynamical processes often exhibit qualitative changes, called bifurcations, like earthquakes, population explosions, stock market crashes, disease outbreaks and so on. Bifurcation theory is a powerful tool to study bifurcation phenomena and explain how small changes in the system parameters can lead to these qualitative changes. The methods of bifurcation theory enable us to identify the parameter values where bifurcations occur, and to predict the changes in behaviour of the system near the bifurcation points. To facilitate the application of bifurcation theory in solving real-world complex problems, which are usually high dimensional and nonlinear, the developments of efficient algorithms and computer programs to reduce system complexity are required. Center manifold theory and normal form theory will be used to greatly simplify system equations by extracting the "key" information (or terms) to form a simple system, while keeping the qualitative behaivour of the system unchanged near bifurcation points. This proposed research program has three objectives. One of them is to develop the theory and efficient computational methods for the parametric normal forms of general delay differential equations, which can be easily used to find, for example, periodic solutions (limit cycles) of a complex system and determine their stability. The other two objectives are focused on applications. We intend to apply the methods of dynamical systems and bifurcation theory with the efficient computational tools to analyze models of specific biological processes: HIV-1 therapy, and recurrent infection. In particular, we shall further study our early developed HIV-1 therapy model to find new mechanisms which can be used to identify other types of viral blips. We also want to apply the bifurcation theory and normal forms for delay differential systems to investigate the blips phenomenon in HIV-1 models with delays. These applications are not only significant for increasing scientific understanding, but progress may yield practical, clinical benefits. In addition, the theory and methodology we develop for these specific applications will be useful for many applications from other disciplines, as mentioned above.
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Yu, Pei其他文献
Mortality risks associated with floods in 761 communities worldwide: time series study.
- DOI:
10.1136/bmj-2023-075081 - 发表时间:
2023-10-04 - 期刊:
- 影响因子:105.7
- 作者:
Yang, Zhengyu;Huang, Wenzhong;Mckenzie, Joanne E.;Xu, Rongbin;Yu, Pei;Ye, Tingting;Wen, Bo;Gasparrini, Antonio;Armstrong, Ben;Tong, Shilu;Lavigne, Eric;Madureira, Joana;Kysely, Jan;Guo, Yuming;Li, Shanshan;MCC Collaborative Res Network - 通讯作者:
MCC Collaborative Res Network
Research on Movement of Fluid Stratification Interface in Density Lock
密度锁中流体层界面运动研究
- DOI:
- 发表时间:
2010 - 期刊:
- 影响因子:0
- 作者:
Yan, Chang-Qi;Gu, Hai-Feng;Yu, Pei - 通讯作者:
Yu, Pei
Cranial irradiation impairs intrinsic excitability and synaptic plasticity of hippocampal CA1 pyramidal neurons with implications for cognitive function.
- DOI:
10.4103/1673-5374.336875 - 发表时间:
2022-10 - 期刊:
- 影响因子:6.1
- 作者:
Wu, Min-Yi;Zou, Wen-Jun;Yu, Pei;Yang, Yuhua;Li, Shao-Jian;Liu, Qiang;Xie, Jiatian;Chen, Si-Qi;Lin, Wei-Jye;Tang, Yamei - 通讯作者:
Tang, Yamei
Does the emissions trading system in developing countries accelerate carbon leakage through OFDI? Evidence from China
- DOI:
10.1016/j.eneco.2021.105397 - 发表时间:
2021-06-22 - 期刊:
- 影响因子:12.8
- 作者:
Yu, Pei;Cai, Zhengfang;Sun, Yongping - 通讯作者:
Sun, Yongping
Bifurcation analysis of an SIRS epidemic model with a generalized nonmonotone and saturated incidence rate
具有广义非单调和饱和发病率的 SIRS 流行病模型的分岔分析
- DOI:
10.1016/j.jde.2019.03.005 - 发表时间:
2019-07-15 - 期刊:
- 影响因子:2.4
- 作者:
Lu, Min;Huang, Jicai;Yu, Pei - 通讯作者:
Yu, Pei
Yu, Pei的其他文献
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{{ truncateString('Yu, Pei', 18)}}的其他基金
Complex Dynamics in Biological Systems: A Bifurcation Theory Approach
生物系统中的复杂动力学:分岔理论方法
- 批准号:
RGPIN-2020-06414 - 财政年份:2022
- 资助金额:
$ 1.46万 - 项目类别:
Discovery Grants Program - Individual
Complex Dynamics in Biological Systems: A Bifurcation Theory Approach
生物系统中的复杂动力学:分岔理论方法
- 批准号:
RGPIN-2020-06414 - 财政年份:2021
- 资助金额:
$ 1.46万 - 项目类别:
Discovery Grants Program - Individual
Complex Dynamics in Biological Systems: A Bifurcation Theory Approach
生物系统中的复杂动力学:分岔理论方法
- 批准号:
RGPIN-2020-06414 - 财政年份:2020
- 资助金额:
$ 1.46万 - 项目类别:
Discovery Grants Program - Individual
Bifurcation theory, computation and applications
分岔理论、计算与应用
- 批准号:
RGPIN-2015-06210 - 财政年份:2019
- 资助金额:
$ 1.46万 - 项目类别:
Discovery Grants Program - Individual
Bifurcation theory, computation and applications
分岔理论、计算与应用
- 批准号:
RGPIN-2015-06210 - 财政年份:2018
- 资助金额:
$ 1.46万 - 项目类别:
Discovery Grants Program - Individual
Bifurcation theory, computation and applications
分岔理论、计算与应用
- 批准号:
RGPIN-2015-06210 - 财政年份:2016
- 资助金额:
$ 1.46万 - 项目类别:
Discovery Grants Program - Individual
Bifurcation theory, computation and applications
分岔理论、计算与应用
- 批准号:
RGPIN-2015-06210 - 财政年份:2015
- 资助金额:
$ 1.46万 - 项目类别:
Discovery Grants Program - Individual
Computation of center manifold and normal form and application
中心流形和范式的计算及应用
- 批准号:
183636-2010 - 财政年份:2014
- 资助金额:
$ 1.46万 - 项目类别:
Discovery Grants Program - Individual
Computation of center manifold and normal form and application
中心流形和范式的计算及应用
- 批准号:
183636-2010 - 财政年份:2013
- 资助金额:
$ 1.46万 - 项目类别:
Discovery Grants Program - Individual
Computation of center manifold and normal form and application
中心流形和范式的计算及应用
- 批准号:
183636-2010 - 财政年份:2012
- 资助金额:
$ 1.46万 - 项目类别:
Discovery Grants Program - Individual
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