138 research outputs found
Bounding network spectra for network design
The identification of the limiting factors in the dynamical behavior of
complex systems is an important interdisciplinary problem which often can be
traced to the spectral properties of an underlying network. By deriving a
general relation between the eigenvalues of weighted and unweighted networks,
here I show that for a wide class of networks the dynamical behavior is tightly
bounded by few network parameters. This result provides rigorous conditions for
the design of networks with predefined dynamical properties and for the
structural control of physical processes in complex systems. The results are
illustrated using synchronization phenomena as a model process.Comment: 17 pages, 4 figure
Chaos at Fifty
In 1963 Edward Lorenz revealed deterministic predictability to be an illusion
and gave birth to a field that still thrives. This Feature Article discusses
Lorenz's discovery and developments that followed from it.Comment: For an animated visualization of the Lorenz attractor, click here
http://www.youtube.com/watch?v=iu4RdmBVdp
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