Boolean Dynamics with Random Couplings
By Leo P. Kadanoff, Susan N. Coppersmith, Maximino Aldana. 2002
343 citations recorded by the source corpus.
This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the sizes of their basins of attraction, and the flow of information through the systems. In the limit of infinite N, there is a phase transition between a chaotic and an ordered phase, with a critical phase in between. We argue that the behavior of this system depends significantly on the topology of the network connections. If the elements are placed upon a lattice with dimension d,the system shows correlations related to the standard percolation or directed percolation phase transition on such a lattice. On the other hand, a very different behavior is seen in the Kauffman net in which all spins are equally likely to be coupled to a given spin. In this situation, coupling loops are mostly suppressed, and the behavior of the system is much more like that of a mean field theory. We also describe possible applications of the models to, for example, genetic networks, cell differentiation, evolution, democracy in social systems and neural networks.
Subfields: Computational Theory and Mathematics, Condensed Matter Physics, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/12aa6004b080d937bc0e9c9f640880eb22a7fb11
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Condensed Matter Physics
In Molecular Biology
Citations in the corpus
- Boolean dynamics of networks with scale-free topology (2003, background): “5 However, a great deal of numerical work has been done to understand the structure of the configuration space of the Kauffman model (for references see [5]).”