Simple dynamics on graphs

@article{Gadouleau2016SimpleDO,
  title={Simple dynamics on graphs},
  author={Maximilien Gadouleau and Adrien Richard},
  journal={ArXiv},
  year={2016},
  volume={abs/1503.04688}
}

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References

SHOWING 1-10 OF 31 REFERENCES

Boolean Monomial Dynamical Systems

Abstract.An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over

The Dynamics of Conjunctive and Disjunctive Boolean Network Models

A sharp lower bound and an upper bound on the number of limit cycles of a given length are provided, in terms of properties of the partially ordered set of strongly connected components.

Maximum Number of Fixed Points in Regulatory Boolean Networks

  • J. Aracena
  • Mathematics
    Bulletin of mathematical biology
  • 2008
An upper bound for the number of fixed points in a particular class of BNs called regulatory Boolean networks is exhibited in terms of minimum cardinality of a set of vertices meeting all positive cycles of the network, which can be applied in the design of genetic regulatory networks.

Sequential operator for filtering cycles in Boolean networks

Discrete iterations - a metric study

  • F. Robert
  • Mathematics
    Springer series in computational mathematics
  • 1986

Digraphs - theory, algorithms and applications

Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science, and it will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

Iterative behaviour of generalized majority functions

A combinatorial analogue of the Jacobian problem in automata networks