440 research outputs found
Data based identification and prediction of nonlinear and complex dynamical systems
We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin
Chaotic dynamics of electric-field domains in periodically driven superlattices
Self-sustained time-dependent current oscillations under dc voltage bias have
been observed in recent experiments on n-doped semiconductor superlattices with
sequential resonant tunneling. The current oscillations are caused by the
motion and recycling of the domain wall separating low- and high-electric-
field regions of the superlattice, as the analysis of a discrete drift model
shows and experimental evidence supports. Numerical simulation shows that
different nonlinear dynamical regimes of the domain wall appear when an
external microwave signal is superimposed on the dc bias and its driving
frequency and driving amplitude vary. On the frequency - amplitude parameter
plane, there are regions of entrainment and quasiperiodicity forming Arnol'd
tongues. Chaos is demonstrated to appear at the boundaries of the tongues and
in the regions where they overlap. Coexistence of up to four electric-field
domains randomly nucleated in space is detected under ac+dc driving.Comment: 9 pages, LaTex, RevTex. 12 uuencoded figures (1.8M) should be
requested by e-mail from the autho
Theoretical and computational advances in nonlinear dynamical systems 2018
Peer reviewedPublisher PD
Time Quasilattices in Dissipative Dynamical Systems
We establish the existence of `time quasilattices' as stable trajectories in
dissipative dynamical systems. These tilings of the time axis, with two unit
cells of different durations, can be generated as cuts through a periodic
lattice spanned by two orthogonal directions of time. We show that there are
precisely two admissible time quasilattices, which we term the infinite Pell
and Clapeyron words, reached by a generalization of the period-doubling
cascade. Finite Pell and Clapeyron words of increasing length provide
systematic periodic approximations to time quasilattices which can be verified
experimentally. The results apply to all systems featuring the universal
sequence of periodic windows. We provide examples of discrete-time maps, and
periodically-driven continuous-time dynamical systems. We identify quantum
many-body systems in which time quasilattices develop rigidity via the
interaction of many degrees of freedom, thus constituting dissipative discrete
`time quasicrystals'.Comment: 38 pages, 14 figures. This version incorporates "Pell and Clapeyron
Words as Stable Trajectories in Dynamical Systems", arXiv:1707.09333.
Submission to SciPos
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