TY - JOUR
T1 - Strange nonchaotic attractors in a nonsmooth dynamical system
AU - Li, Gaolei
AU - Yue, Yuan
AU - Xie, Jianhua
AU - Grebogi, Celso
N1 - This work is supported by the National Natural Science Foundation of China (11672249, 11732014 and 11572263).
PY - 2019/11
Y1 - 2019/11
N2 - Strange nonchaotic attractors (SNAs) have fractal geometric structure, but are nonchaotic in the dynamical sense. Since Grebogi et al. discovered SNA in 1984, it has become one of the important topics in nonlinear dynamics. Now, the study of SNAs has been mainly confined to smooth dynamics with quasiperiodic excitation or random excitation. In this paper, we consider a class of single-degree-of-freedom gear dynamical system with quasiperiodic forcing. We show that the gear transmission system can be modeled as a three-dimensional piecewise linear system, which belongs to a typical class of nonsmooth system. We then show that SNAs do exist in such nonsmooth dynamical system with quasiperiodic force. The dynamical behavior of the nonsmooth system is analyzed as a parameter is varied. The dynamics is analyzed through phase diagrams and bifurcation diagrams, Lyapunov exponents, singular continuous power spectrum, phase sensitivity of time series and rational approximations.
AB - Strange nonchaotic attractors (SNAs) have fractal geometric structure, but are nonchaotic in the dynamical sense. Since Grebogi et al. discovered SNA in 1984, it has become one of the important topics in nonlinear dynamics. Now, the study of SNAs has been mainly confined to smooth dynamics with quasiperiodic excitation or random excitation. In this paper, we consider a class of single-degree-of-freedom gear dynamical system with quasiperiodic forcing. We show that the gear transmission system can be modeled as a three-dimensional piecewise linear system, which belongs to a typical class of nonsmooth system. We then show that SNAs do exist in such nonsmooth dynamical system with quasiperiodic force. The dynamical behavior of the nonsmooth system is analyzed as a parameter is varied. The dynamics is analyzed through phase diagrams and bifurcation diagrams, Lyapunov exponents, singular continuous power spectrum, phase sensitivity of time series and rational approximations.
KW - Lyapunov exponent
KW - Nonsmooth dynamical system
KW - Phase sensitive property
KW - Strange nonchaotic attractors
UR - http://www.scopus.com/inward/record.url?scp=85067186513&partnerID=8YFLogxK
UR - http://www.mendeley.com/research/strange-nonchaotic-attractors-nonsmooth-dynamical-system
U2 - 10.1016/j.cnsns.2019.104858
DO - 10.1016/j.cnsns.2019.104858
M3 - Article
AN - SCOPUS:85067186513
VL - 78
JO - Communications in Nonlinear Science & Numerical Simulation
JF - Communications in Nonlinear Science & Numerical Simulation
SN - 1007-5704
M1 - 104858
ER -