## [Reaction–Diffusion System](/reaction-diffusion-system-0) Definition A class of continuum models in which one or more scalar fields representing concentrations evolve under local nonlinear reaction kinetics coupled to spatial spreading by diffusion, commonly written as time-dependent partial differential equations. ## Principle Principle Local production/consumption terms change field values while diffusive transport redistributes them; the interplay of nonlinearity and spatial coupling organizes spatial and temporal structure. ## Demonstration Demonstration An activator–inhibitor pair with an activator that autocatalyses and a faster-diffusing inhibitor produces stationary stripe or spot patterns when parameters place the system in the pattern-forming regime. ## Misapplication Misapplication Treating a reaction–diffusion description as valid for a network of discrete compartments with negligible exchange leads to incorrect predictions of pattern scale and stability. ## Consequence Consequence When applied correctly, the framework predicts emergent spatial structures (steady patterns, traveling waves, oscillatory media) and yields parameter-dependent length and time scales. ## Reversal Reversal Pure diffusion without reactive terms, which only smooths gradients and cannot sustain self-organized spatial structure. ## Boundary Boundary Applies to media where molecular/agent motion is well represented by diffusive transport and continuum concentrations; excludes dominance by directed flow, ballistic transport, or strictly discrete-agent dynamics. ## Semantic Tension Semantic Tension Sits between spatially homogeneous kinetic models and transport-dominated equations; debate centers on whether observed structure stems primarily from local kinetics or from transport coupling. ## Synthesis Synthesis A reaction–diffusion system couples local nonlinear transformation of fields with diffusive spatial coupling to produce macroscopic spatial–temporal patterns in continuous media.