Wright分数阶时滞微分方程的离散化过程  

On discretization process of fractional-order delay Wright equation

作　　者：刘杉杉 高飞[1] Liu Shanshan;Gao Fei(School of Sciences,Wuhan University of Technology,Wuhan 430070,China)

机构地区：[1]武汉理工大学理学院

出　　处：《计算机应用研究》2019年第8期2383-2387,共5页Application Research of Computers

基　　金：国家自然科学基金重大研究计划资助项目(91324201);湖北省自然科学基金资助项目(2014CFB865)

摘　　要：引进了一种离散化方法对分数阶时滞微分方程进行离散化求解。首先考察Wright分数阶时滞微分方程;其次分析相应具有分段常数变元的Wright分数阶时滞微分方程,并应用离散化过程对模型进行数值求解;然后根据不动点理论讨论该合成动力系统不动点的稳定性;最后借助MATLAB对模型进行数值仿真,并结合Lyapunov指数、相图、时间序列图、分岔图探讨模型更多复杂的动力学现象。结果显示,提出方法成功地对Wright分数阶时滞微分方程进行了离散。This paper introduced a discretization process to discretize fractional- order delay differential equations. First of all, it considered the fractional- order delay Wright fractional differential equation. Then, it analyzed the corresponding fractional-order Wright differential equation with piecewise constant arguments and applied the proposed discretization process to solve the model numerically. After that, according to the fixed points theory, this paper investigated the stability of the fixed points of the resultant dynamical system. Finally, it carried out a numerical simulation including Lyapunov exponent, phase diagrams, time series diagram, bifurcation using MATLAB to reveal more complex dynamics of the model. Simulation experiments show that this paper succeeds in discretizing fractional-order delay Wright equation.

关 键 词：分数阶微分方程 时滞 分段常数变元 定点 分岔 混沌 

分 类 号：TP301.5[自动化与计算机技术—计算机系统结构]