On a fractional-order delay Mackey-Glass equation

Advances in Difference Equations

Ahmed MA El-Sayed¹  Sanaa M Salman²  Naemaa A Elabd³ 

[1] Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt;Faculty of Education, Alexandria University, Alexandria, Egypt;Faculty of Science, Alexandria University, Alexandria, Egypt

关键词: fractional-order delay Mackey-Glass equations;    fixed points;    local stability;    discretization;    Lyapunov exponent;    bifurcation;    chaos;   

DOI  :  10.1186/s13662-016-0863-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, a fractional-order Mackey-Glass equation with constant delay is considered. The local stability of the fixed points is analyzed. Moreover, a discretization process is applied to convert the fractional-order delay equation to its discrete analog. A numerical simulation including Lyapunov exponent, phase diagrams, bifurcation, and chaos is carried out using Matlab to ensure theoretical results and to reveal more complex dynamics of the equation after discretization.

【 授权许可】

CC BY