Self-organized critical random Boolean networks

Luque, Bartolo; Ballesteros, Fernando J.; Muro, Enrique M.

doi:10.1103/physreve.63.051913

Cited by 19 publications

(20 citation statements)

References 21 publications

(35 reference statements)

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“…Note that this genuine adaptive network effect can be observed in networks where topological evolution and dynamics of the states take place on separate time scales, as shown in the example presented by Bornholdt & Rohlf. These results inspired several subsequent investigations that extended the results (Bornholdt & Sneppen 1998Luque et al 2001;Kamp & Bornholdt 2002;Bornholdt & Röhl 2003;Liu & Bassler 2006;Rohlf 2007).…”

Section: K3supporting

confidence: 65%

Adaptive coevolutionary networks: a review

Groß

Blasius²

2007

J. R. Soc. Interface.

886

778

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Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel studies from different fields, ranging from genomics to game theory. Here we review these recent developments and show that they can be viewed from a unique angle. We demonstrate that all these studies are characterized by common themes, most prominently: complex dynamics and robust topological self-organization based on simple local rules.

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Section: K3supporting

confidence: 65%

Adaptive coevolutionary networks: a review

Groß

Blasius²

2007

J. R. Soc. Interface.

886

778

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“…Boolean networks [1,2,3,4,5,6,7,8] have been extensively studied over the past three decades. They have applications as models of gene regulatory networks, and also as models of social and economic systems.…”

Section: Introductionmentioning

confidence: 99%

Emergent criticality from coevolution in random Boolean networks

2006

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The co-evolution of network topology and dynamics is studied in an evolutionary Boolean network model that is a simple model of gene regulatory network. We find that a critical state emerges spontaneously resulting from interplay between topology and dynamics during the evolution. The final evolved state is shown to be independent of initial conditions. The network appears to be driven to a random Boolean network with uniform in-degree of two in the large network limit. However, for biologically realized network sizes, significant finite-size effects are observed including a broad in-degree distribution and an average in-degree connection between two and three. These results may be important for explaining properties of gene regulatory networks.

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“…The mutations affect the connections and the update functions of the nodes. Compared to the simulations in [8,9,10,11,12,13,14,15,16], fitness can be changed by more types of mutations in our model. We let the networks evolve freely under a biologically motivated fitness criterion without imposing any "target properties" to find network topologies that are evolutionary robust.…”

Section: Introductionmentioning

confidence: 99%

“…Further studies of the model [13] showed that the evolved networks are highly canalized. Other models that evolve to a critical state are studied in [14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Evolution of canalizing Boolean networks

Szejka¹,

Drossel²

2007

Eur. Phys. J. B

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Boolean networks with canalizing functions are used to model gene regulatory networks. In order to learn how such networks may behave under evolutionary forces, we simulate the evolution of a single Boolean network by means of an adaptive walk, which allows us to explore the fitness landscape. Mutations change the connections and the functions of the nodes. Our fitness criterion is the robustness of the dynamical attractors against small perturbations. We find that with this fitness criterion the global maximum is always reached and that there is a huge neutral space of 100% fitness. Furthermore, in spite of having such a high degree of robustness, the evolved networks still share many features with "chaotic" networks.

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Self-organized critical random Boolean networks

Cited by 19 publications

References 21 publications

Adaptive coevolutionary networks: a review

Adaptive coevolutionary networks: a review

Emergent criticality from coevolution in random Boolean networks

Evolution of canalizing Boolean networks

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