Open AccessNew periodic-chaotic attractors in slow-fast Duffing system with periodic parametric excitation
Author(s) -
Xianghong Li,
Yongjun Shen,
JianQiao Sun,
Shaopu Yang
Publication year - 2019
Publication title -
scientific reports
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.24
H-Index - 213
ISSN - 2045-2322
DOI - 10.1038/s41598-019-46768-7
Subject(s) - attractor , lyapunov exponent , chaotic , duffing equation , fixed point , chaotic hysteresis , periodic function , parametric statistics , physics , control of chaos , nonlinear system , mathematical analysis , synchronization of chaos , statistical physics , mathematics , control theory (sociology) , computer science , quantum mechanics , statistics , control (management) , artificial intelligence
A new type of responses called as periodic-chaotic motion is found by numerical simulations in a Duffing oscillator with a slowly periodically parametric excitation. The periodic-chaotic motion is an attractor, and simultaneously possesses the feature of periodic and chaotic oscillations, which is a new addition to the rich nonlinear motions of the Duffing system including equlibria, periodic responses, quasi-periodic oscillations and chaos. In the current slow-fast Duffing system, we find three new attractors in the form of periodic-chaotic motions. These are called the fixed-point chaotic attractor, the fixed-point strange nonchaotic attractor, and the critical behavior with the maximum Lyapunov exponent fluctuating around zero. The system periodically switches between one attractor with a fixed single-well potential and the other with time-varying two-well potentials in every period of excitation. This behavior is apparently the mechanism to generate the periodic-chaotic motion.