Boolean Network - Classical Model - Attractors

Attractors

Since a Boolean network has only 2N possible states, a trajectory will sooner or later reach a previously visited state, and thus, since the dynamics are deterministic, the trajectory will fall into a cycle. In the literature in this field, each cycle is also called an attractor (though in the broader field of dynamical systems a cycle is only an attractor if purturbations from it lead back to it). If the attractor has only a single state it is called a point attractor, and if the attractor consists of more than one state it is called a cycle attractor. The set of states that lead to an attractor is called the basin of the attractor. States which occur only at the beginning of trajectories (no trajectories lead to them), are called garden-of-Eden states and the dynamics of the network flow from these states towards attractors. The time it takes to reach an attractor is called transient time. (Gershenson 2004)