Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noise Response Data Reveal Novel Controllability Gramian for Nonlinear
  Network Dynamics   Control of nonlinear large-scale dynamical networks, e.g., collective
behavior of agents interacting via a scale-free connection topology, is a
central problem in many scientific and engineering fields. For the linear
version of this problem, the so-called controllability Gramian has played an
important role to quantify how effectively the dynamical states are reachable
by a suitable driving input. In this paper, we first extend the notion of the
controllability Gramian to nonlinear dynamics in terms of the Gibbs
distribution. Next, we show that, when the networks are open to environmental
noise, the newly defined Gramian is equal to the covariance matrix associated
with randomly excited, but uncontrolled, dynamical state trajectories. This
fact theoretically justifies a simple Monte Carlo simulation that can extract
effectively controllable subdynamics in nonlinear complex networks. In
addition, the result provides a novel insight into the relationship between
controllability and statistical mechanics.

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The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg