• 应用前沿、交叉与综合 •

### 二维Logistic分数阶微分方程的离散化过程

1. 武汉理工大学 理学院, 武汉 430070
• 收稿日期:2018-04-25 修回日期:2018-06-11 出版日期:2019-01-10 发布日期:2019-01-21
• 通讯作者: 高飞
• 作者简介:刘杉杉(1992-),女,河北邯郸人,硕士研究生,主要研究方向:分数阶微分方程、分数阶混沌系统;高飞(1976-),男,湖北武汉人,教授,博士,主要研究方向:群集智能、演化计算、量子智能算法、混沌控制与同步;李文琴(1995-),女,河南三门峡人,硕士研究生,主要研究方向:分数阶微分方程、分数阶混沌系统。
• 基金资助:
中央高校基本科研业务费专项资金资助项目（181114011，185214003，2018-zy-137）；国家自然科学基金重大研究计划项目（91324201）；湖北省自然科学基金资助项目（2014CFB865）。

### Discretization process of coupled Logistic fractional-order differential equation

1. School of Science, Wuhan University of Technology, Wuhan Hubei 430070, China
• Received:2018-04-25 Revised:2018-06-11 Online:2019-01-10 Published:2019-01-21
• Supported by:
This work is partially supported by the Fundamental Research Funds for the Central Universities (181114011, 185214003, 2018-zy-137), the Major Research Projects of National Natural Science Foundation of China (91324201), and the Natural Science Foundation of Hubei Province (2014CFB865).

Abstract: Focusing on the problem of solving coupled Logistic fractional-order differential equation, a discretization method was introduced to solve it discretly. Firstly, a coupled Logistic integer-order differential equation was introduced into the fields of fractional-order calculus. Secondly, the corresponding coupled Logistic fractional-order differential equation with piecewise constant arguments was analyzed and the proposed discretization method was applied to solve the model numerically. Then, according to the fixed point theory, the stability of the fixed point of the synthetic dynamic system was discussed, and the boundary equation of the first bifurcation of the coupled Logistic fractional-order system in the parameter space was given. Finally, the model was numerically simulated by Matlab, and more complex dynamics phenomena of model were discussed with Lyapunov index, phase diagram, time series diagram and bifurcation diagram. The simulation results show that, the proposed method is successful in discretizing coupled Logistic fractional-order differential equation.