Numerical scheme and dynamic analysis for variable-order fractional van der Pol model of nonlinear economic cycle

Advances in Difference Equations

Lei He¹  Pei Tang¹  Li Yi¹ 

[1]Business College, Hunan Normal University, Changsha, China

关键词: van der Pol model;    variable-order fractional derivative;    dynamic behavior;    26A33;    34A08;   

DOI  :  10.1186/s13662-016-0920-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Considering the fact that the memory in economic series changes with dynamic economic environment, this paper is devoted to the proposal of a variable-order fractional van der Pol model (VOFVDPM), where the order of the derivative is replaced by a time-dependent function. A numeric scheme for this model is designed by the Adams-Bashforth-Moulton method. The dynamic behaviors of the VOFVDPM with linear and periodic variable-order functions are investigated through numerical experiment. Some dynamic characteristics of the VOFVDPM that do not exist in a fractional order van der Pol model are discovered in the numerical simulation, such as existing limit point when the linear order functions have the same ranges and opposite slopes.

【 授权许可】

CC BY