A Boolean network consists of a discrete set of Boolean variables each of which has a boolean function (possibly different for each varible) assigned to it which takes inputs from a subset of those variables and output that determines the state of the variable it is assigned to. This set of functions in effect determines a topology (connectivity) on the set of variables, which then become nodes in a network. Usually, the dynamics of the system is taken as a discrete time series where the state of the entire network at time t+1 is determined by evaluating each variable's function on the state of the network at time t. This may be done synchronously or asynchronously.
A boolean network is a particular kind of sequential dynamical system, where time and states are discrete, i.e. both the set of variables and the set of states in the time series each have a bijection onto an integer series. Boolean networks are related to cellular automata. Usually, cellular automata are defined with an homogenous topology, i.e. a single line of nodes, a square or hexagonal grid of nodes or an even higher dimensional structure, but each variable (node in the grid) may take on more than two values (and hence not be boolean).
A random Boolean network is one that is randomly selected from the set of all possible boolean networks of a particular size, N. One then can study statistically, how the expected properties of such networks depend on various statistical properties of the ensemble of all possible networks. I.e. how does the behavior change as the average connectivity is changed.
Read more about Boolean Network: Classical Model, Topologies, Updating Schemes, Applications
Famous quotes containing the word network:
“How have I been able to live so long outside Nature without identifying myself with it? Everything lives, moves, everything corresponds; the magnetic rays, emanating either from myself or from others, cross the limitless chain of created things unimpeded; it is a transparent network that covers the world, and its slender threads communicate themselves by degrees to the planets and stars. Captive now upon earth, I commune with the chorus of the stars who share in my joys and sorrows.”
—Gérard De Nerval (1808–1855)