The Kauffman model on small-world topology

Ferraz, Carlos Handrey Araujo; Herrmann, Hans J.

doi:10.1016/j.physa.2006.04.063

Cited by 6 publications

(3 citation statements)

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“…Once it was proved that the average number of attractors in an RBN grows faster than any power law with network size [22], the scaling behaviors of the number and size of attractors for BNs with different topologies and distributions of Boolean functions were determined [23][24][25][26]. In this manner, interest in BNs with special topologies, including small-world [27] and scale-free [28][29][30] networks, has increased.…”

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confidence: 99%

Expected Number of Fixed Points in Boolean Networks with Arbitrary Topology

Mori

2017

Phys. Rev. Lett.

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Boolean network models describe genetic, neural, and social dynamics in complex networks, where the dynamics depend generally on network topology. Fixed points in a genetic regulatory network are typically considered to correspond to cell types in an organism. We prove that the expected number of fixed points in a Boolean network, with Boolean functions drawn from probability distributions that are not required to be uniform or identical, is one, and is independent of network topology if only a feedback arc set satisfies a stochastic neutrality condition. We also demonstrate that the expected number is increased by the predominance of positive feedback in a cycle.

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confidence: 99%

Expected Number of Fixed Points in Boolean Networks with Arbitrary Topology

Mori

2017

Phys. Rev. Lett.

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“…[8]. The same thing also happens if one regards the smallworld case [19]. On the other hand, the damage spreading on square lattices is quite sensitive to the removal of connections.…”

Section: Numerical Resultsmentioning

confidence: 88%

“…For more details about this rewiring procedure as well as a phase transiton and fractality in the Kauffman model on smallworld topology, the reader should consult Ref. [19]. In the present work, we have regarded both the quenched and the annealed version.…”

Section: Computational Proceduresmentioning

confidence: 99%

The strange man in random networks of automata

Ferraz

Herrmann

2008

Physica A: Statistical Mechanics and its Applications

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We have performed computer simulations of Kauffman's automata on several graphs such as the regular square lattice and invasion percolation clusters in order to investigate phase transitions, radial distributions of the mean total damage (dynamical exponent z) and propagation speeds of the damage when one adds a damaging agent, nicknamed "strange man". Despite the increase in the damaging efficiency, we have not observed any appreciable change at the transition threshold to chaos neither for the short-range nor for the small-world case on the square lattices when the strange man is added in comparison to when small initial damages are inserted in the system. The propagation speed of the damage cloud until touching the border of the system in both cases obeys a power law with a critical exponent α that strongly depends on the lattice. Particularly, we have ckecked the damage spreading when some connections are removed on the square lattice and when one considers special invasion percolation clusters (high boundary-saturation clusters). It is seen that the propagation speed in these systems is quite sensible to the degree of dilution.

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Kauffman Cellular Automata on Quasicrystal Topology

Ferraz

Lima

2018

Braz J Phys

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The Kauffman model on small-world topology

Cited by 6 publications

References 19 publications

Expected Number of Fixed Points in Boolean Networks with Arbitrary Topology

Expected Number of Fixed Points in Boolean Networks with Arbitrary Topology

The strange man in random networks of automata

Kauffman Cellular Automata on Quasicrystal Topology

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