Boolean network

A Boolean network is a directed system of binary-valued variables whose values update according to Boolean functions of other variables. It models how discrete states change over time.

Boolean function: A function that maps binary inputs to a binary output using logical operations. Each node’s update rule is a Boolean function of selected network variables.
Boolean variable: A variable restricted to two values, commonly represented as 0 and 1. Every network component has one of these two possible states.
Gene regulatory network: A network of genes and regulatory molecules that controls gene expression. Boolean networks approximate genes as on or off and encode regulatory influences as update rules.
Stuart Kauffman: A biologist known for foundational work on random Boolean networks and biological self-organization. His models helped establish Boolean networks as a way to study gene regulation.
Ordinary differential equation: An equation relating a quantity to its rate of change with respect to one independent variable. Differential-equation models represent continuous concentrations that Boolean networks reduce to two states.
Synchronous updating: A discrete-time update scheme in which every variable changes simultaneously at each time step. It defines one common timing convention for evolving a Boolean network.
Directed graph: A graph whose edges connect ordered pairs of vertices. Its edges encode which variables can influence which others.
Cellular differentiation: The process by which cells acquire distinct structures and functions. Stable network states can represent distinct cellular identities.
Random Boolean network: A Boolean network whose connections and update functions are assigned through a random model. Kauffman used this network class to explore how regulatory systems can produce ordered dynamics.
Petri net: A mathematical model of systems using places, transitions, and tokens to represent state and events. Petri nets offer an alternative discrete framework with explicit event and resource structure.

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Cellular automatonCompared with: It uses discrete rules like an automaton, but its connections need not form a regular grid.