Chaotic vibrations of the duffing system with fractional damping.
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.
Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, PL-20-618 Lublin, Poland.
Arkadiusz
A
Syta
Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, PL-20-618 Lublin, Poland.
Grzegorz
G
Litak
Department of Civil and Building Engineering, and Architecture, Polytechnic University of Marche, 60131 Ancona, Italy.
Stefano
S
Lenci
Institut für Festkörpermechanik, Technische Universität Dresden, 01062 Dresden, Germany.
Michael
M
Scheffler