895 research outputs found
Output functions and fractal dimensions in dynamical systems
We present a novel method for the calculation of the fractal dimension of
boundaries in dynamical systems, which is in many cases many orders of
magnitude more efficient than the uncertainty method. We call it the Output
Function Evaluation (OFE) method. The OFE method is based on an efficient
scheme for computing output functions, such as the escape time, on a
one-dimensional portion of the phase space. We show analytically that the OFE
method is much more efficient than the uncertainty method for boundaries with
, where is the dimension of the intersection of the boundary with a
one-dimensional manifold. We apply the OFE method to a scattering system, and
compare it to the uncertainty method. We use the OFE method to study the
behavior of the fractal dimension as the system's dynamics undergoes a
topological transition.Comment: Uses REVTEX; to be published in Phys. Rev. Let
Variation of the Dependence of the Transient Process Duration on the Initial Conditions in Systems with Discrete Time
Dependence of the transient process duration on the initial conditions is
considered in one- and two-dimensional systems with discrete time, representing
a logistic map and the Eno map, respectively.Comment: 4 pages, 2 figure
Robust Chaos
It has been proposed to make practical use of chaos in communication, in
enhancing mixing in chemical processes and in spreading the spectrum of
switch-mode power suppies to avoid electromagnetic interference. It is however
known that for most smooth chaotic systems, there is a dense set of periodic
windows for any range of parameter values. Therefore in practical systems
working in chaotic mode, slight inadvertent fluctuation of a parameter may take
the system out of chaos. We say a chaotic attractor is robust if, for its
parameter values there exists a neighborhood in the parameter space with no
periodic attractor and the chaotic attractor is unique in that neighborhood. In
this paper we show that robust chaos can occur in piecewise smooth systems and
obtain the conditions of its occurrence. We illustrate this phenomenon with a
practical example from electrical engineering.Comment: 4 pages, Latex, 4 postscript figures, To appear in Phys. Rev. Let
General analytical solutions for DC/AC circuit-network analysis
All authors thank the Scottish University Physics Alliance (SUPA) support. NR also acknowledges de support of PEDECIBA, Uruguay. MSB acknowledges the support of EPSRC grant Ref. EP/I032606/1. Open access via Springer Compact Agreement.Peer reviewedPublisher PD
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
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