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Deterministic system (mathematics) Linear system; Partial differential equation; Dynamical systems and chaos theory; Chaos theory. Chaos argument; Butterfly effect; 0-1 test for chaos; Bifurcation diagram; Feigenbaum constant; Sharkovskii's theorem; Attractor. Strange nonchaotic attractor; Stability theory. Mechanical equilibrium; Astable ...
System dynamics is a methodology and mathematical modeling technique to frame, understand, and discuss complex issues and problems. Originally developed in the 1950s to help corporate managers improve their understanding of industrial processes, SD is currently being used throughout the public and private sector for policy analysis and design.
Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems.Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does ...
Dynamic simulation (or dynamic system simulation) is the use of a computer program to model the time-varying behavior of a dynamical system. The systems are typically described by ordinary differential equations or partial differential equations. A simulation run solves the state-equation system to find the behavior of the state variables over ...
A system archetype is a pattern of behavior of a system. Systems expressed by circles of causality have therefore similar structure. Identifying a system archetype and finding the leverage enables efficient changes in a system. The basic system archetypes and possible solutions of the problems are mentioned in the Examples section. [1]
A discrete dynamical system, discrete-time dynamical system is a tuple (T, M, Φ), where M is a manifold locally diffeomorphic to a Banach space, and Φ is a function. When T is taken to be the integers, it is a cascade or a map. If T is restricted to the non-negative integers we call the system a semi-cascade. [14]
The field of system identification uses statistical methods to build mathematical models of dynamical systems from measured data. [1] System identification also includes the optimal design of experiments for efficiently generating informative data for fitting such models as well as model reduction.
The development was initiated by a group of active system dynamics modellers who had needs and ideas for an open toolset. The new needs for features like hierarchical modules, module libraries, collaborative model development and efficient model communication in system dynamics together with the development of open source modelling framework Simantics and simulation environment OpenModelica [4 ...