Chaotic vibrations of the duffing system with fractional damping
Arkadiusz SytaFaculty of Mechanical Engineering, Lublin University of Technology 1 , Nadbystrzycka 36, PL-20-618 Lublin, PolandGrzegorz LitakFaculty of Mechanical Engineering, Lublin University of Technology 1 , Nadbystrzycka 36, PL-20-618 Lublin, PolandStefano LenciDepartment of Civil and Building Engineering, and Architecture, Polytechnic University of Marche 2 , 60131 Ancona, ItalyMichael SchefflerInstitut für Festkörpermechanik, Technische Universität Dresden 3 , 01062 Dresden, Germany
2014en
ABI
Аннотация
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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