Discretization of forced Duffing system with fractional-order damping

Advances in Difference Equations

Ahmed MA El-Sayed¹  Sanaa M Salman²  Zaki FE El-Raheem² 

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

关键词: Duffing oscillator;    fractional-order damping;    fixed points;    stability;    chaotic attractor;    bifurcation;    chaos;   

DOI  :  10.1186/1687-1847-2014-66

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper we are interested in studying the effect of the fractional-order damping in the forced Duffing oscillator before and after applying a discretization process to it. Fixed points and their stability are discussed for the discrete system obtained. Finally, numerical simulations using Matlab are carried out to investigate the dynamic behavior such as bifurcation, chaos, and chaotic attractors. We note that on increasing the value of the fractional-order parameter, the resulting discrete system is stabilized.

【 授权许可】

CC BY