Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modulus Consensus over Networks with Antagonistic Interactions and
  Switching Topologies   In this paper, we study the discrete-time consensus problem over networks
with antagonistic and cooperative interactions. Following the work by Altafini
[IEEE Trans. Automatic Control, 58 (2013), pp. 935--946], by an antagonistic
interaction between a pair of nodes updating their scalar states we mean one
node receives the opposite of the state of the other and naturally by an
cooperative interaction we mean the former receives the true state of the
latter. Here the pairwise communication can be either unidirectional or
bidirectional and the overall network topology graph may change with time. The
concept of modulus consensus is introduced to characterize the scenario that
the moduli of the node states reach a consensus. It is proved that modulus
consensus is achieved if the switching interaction graph is uniformly jointly
strongly connected for unidirectional communications, or infinitely jointly
connected for bidirectional communications. We construct a counterexample to
underscore the rather surprising fact that quasi-strong connectivity of the
interaction graph, i.e., the graph contains a directed spanning tree, is not
sufficient to guarantee modulus consensus even under fixed topologies. Finally,
simulation results using a discrete-time Kuramoto model are given to illustrate
the convergence results showing that the proposed framework is applicable to a
class of networks with general nonlinear node dynamics.

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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an