dynamicswhich

dynamicswhich is a theoretical framework that analyzes how dynamic processes give rise to the selection of specific outcomes within a system. It treats the evolution of a state variable as governed by a rule or set of rules, while simultaneously considering a which-outcome selection that determines which among several potential stable states is realized under given conditions. The term emphasizes the role of constraint, initial conditions, and path dependence in shaping realized trajectories.

Core concepts include a dynamical system defined on a state space, a time parameter (discrete or continuous), and a selection operator that maps the current state and possibly external inputs to a preferred or realized outcome. Attractors, basins of attraction, and bifurcations are used to analyze how small changes in conditions can switch which outcome is realized. Stochastic variants introduce probabilistic outcomes, while deterministic versions study unique realizations.

dynamicswhich connects to dynamical systems theory, control theory, and decision science. Unlike standard analyses that focus on the evolution of states alone, dynamicswhich emphasizes the meta-question of which states or outcomes are realized given a set of rules and constraints. It can incorporate game-theoretic or optimization elements to model choice under dynamics, and it is used to study phenomena such as path dependence, hysteresis, and multistability in complex systems.

Applications include ecology and population dynamics, where which states persist under environmental change; economics and social systems, where different market or collective outcomes emerge; and engineering, where system safety depends on the realized operating point. Critics note challenges in defining and measuring the selection function and in distinguishing it from the underlying dynamics.