A Boolean Network (BN) is a discrete mathematical model where nodes represent binary variables (such as 0/OFF or 1/ON) that interact with each other over time according to specific logical rules. Introduced by Stuart Kauffman in 1969, these networks are widely used to simplify and simulate the complex, non-linear dynamics of biological systems—most notably gene regulatory networks—as well as computational processes. Core Components
A Boolean network is formally represented as a directed graph: Nodes (
): Individual elements (e.g., genes or proteins) that hold a binary state. signifies active, present, or expressed; signifies inactive, absent, or repressed.
Edges: Directed links between nodes indicating that one entity regulates or influences another. Update Rules (
): Boolean functions assigned to each node. Using logical operators (AND, OR, NOT), these functions dictate what a node’s next state will be based on the current state of its inputs. Network Dynamics and State Space 5.7 Kauffman Model (Boolean Networks)
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