Syta Arkadiusz, Litak Grzegorz, Lenci Stefano, Scheffler Michael
Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, PL-20-618 Lublin, Poland.
Department of Civil and Building Engineering, and Architecture, Polytechnic University of Marche, 60131 Ancona, Italy.
Chaos. 2014 Mar;24(1):013107. doi: 10.1063/1.4861942.
We examined the Duffing system with a fractional damping term. Calculating the basins of attraction, we demonstrate a broad spectrum of non-linear behaviour connected with sensitivity to the initial conditions and chaos. To quantify dynamical response of the system, we propose the statistical 0-1 test as well as the maximal Lyapunov exponent; the application of the latter encounter a few difficulties because of the memory effect due to the fractional derivative. The results are confirmed by bifurcation diagrams, phase portraits, and Poincaré sections.
我们研究了带有分数阻尼项的杜芬系统。通过计算吸引域，我们展示了一系列与初始条件敏感性和混沌相关的非线性行为。为了量化系统的动力学响应，我们提出了统计0-1检验以及最大Lyapunov指数；由于分数阶导数引起的记忆效应，后者的应用遇到了一些困难。结果通过分岔图、相图和庞加莱截面得到了证实。
