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Published on: August 15, 2014
Chaotic vibrations of the duffing system with fractional damping
Arkadiusz Syta1, Grzegorz Litak1, Stefano Lenci2
1Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, PL-20-618 Lublin, Poland.
Abstract:
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.
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