9,769 research outputs found
Equation-free analysis of a dynamically evolving multigraph
In order to illustrate the adaptation of traditional continuum numerical
techniques to the study of complex network systems, we use the equation-free
framework to analyze a dynamically evolving multigraph. This approach is based
on coupling short intervals of direct dynamic network simulation with
appropriately-defined lifting and restriction operators, mapping the detailed
network description to suitable macroscopic (coarse-grained) variables and
back. This enables the acceleration of direct simulations through Coarse
Projective Integration (CPI), as well as the identification of coarse
stationary states via a Newton-GMRES method. We also demonstrate the use of
data-mining, both linear (principal component analysis, PCA) and nonlinear
(diffusion maps, DMAPS) to determine good macroscopic variables (observables)
through which one can coarse-grain the model. These results suggest methods for
decreasing simulation times of dynamic real-world systems such as
epidemiological network models. Additionally, the data-mining techniques could
be applied to a diverse class of problems to search for a succint,
low-dimensional description of the system in a small number of variables
Adaptive Detection of Instabilities: An Experimental Feasibility Study
We present an example of the practical implementation of a protocol for
experimental bifurcation detection based on on-line identification and feedback
control ideas. The idea is to couple the experiment with an on-line
computer-assisted identification/feedback protocol so that the closed-loop
system will converge to the open-loop bifurcation points. We demonstrate the
applicability of this instability detection method by real-time,
computer-assisted detection of period doubling bifurcations of an electronic
circuit; the circuit implements an analog realization of the Roessler system.
The method succeeds in locating the bifurcation points even in the presence of
modest experimental uncertainties, noise and limited resolution. The results
presented here include bifurcation detection experiments that rely on
measurements of a single state variable and delay-based phase space
reconstruction, as well as an example of tracing entire segments of a
codimension-1 bifurcation boundary in two parameter space.Comment: 29 pages, Latex 2.09, 10 figures in encapsulated postscript format
(eps), need psfig macro to include them. Submitted to Physica
- …