GC: n

CT: A dynamical system consists of an abstract phase space or state space, whose coordinates describe the state at any instant, and a dynamical rule that specifies the immediate future of all state variables, given only the present values of those same state variables. For example the state of a pendulum is its angle and angular velocity, and the evolution rule is Newton’s equation F=ma .
Mathematically, a dynamical system is described by an initial value problem. The implication is that there is a notion of time and that a state at one time evolves to a state or possibly a collection of states at a later time. Thus states can be ordered by time, and time can be thought of as a single quantity.
Dynamical systems are deterministic if there is a unique consequent to every state, or stochastic or random if there is a probability distribution of possible consequents (the idealized coin toss has two consequents with equal probability for each initial state).

S: http://www.scholarpedia.org/article/Dynamical_systems (last access: 29 December 2014)

N: 1. A dynamical system is all about the evolution of something over time. To create a dynamical system we simply need to decide what is the “something” that will evolve over time and what is the rule that specifies how that something evolves with time. In this way, a dynamical system is simply a model describing the temporal evolution of a system.
2. A variety of learning problems in robotics, computer vision and other areas of artificial intelligence can be construed as problems of learning statistical models for dynamical systems from sequential observations. Good dynamical system models allow us to represent and predict observations in these systems, which in turn enables applications such as classification, planning, control, simulation, anomaly detection and forecasting.
3. In the fields of Fluid Mechanics and Hydraulics (Physics), the term “dynamical system” means an abstraction of the concept of a family of solutions to an ordinary differential equation, namely, an action of the real numbers on a topological space satisfying certain “flow” properties.
Synonym: dynamic system.
4. In the field of Physics, “dynamical system” means a process or set of processes whose evolution in time is governed by a set of deterministic physical laws.
The climate system is a dynamical system.
5. In the field of Information Science, “dynamic system” means “an “open system” which changes its “states”.
Narrower term: cybernetic system.

S: 1. http://mathinsight.org/dynamical_system_idea (last access: 29 December 2014). 2. http://www.ri.cmu.edu/publication_view.html?pub_id=6517 (last access: 29 December 2014). 3. TERMIUM PLUS (last access: 29 December 2014). 4 & 5. GDT (last access: 29 December 2014).

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CR: artificial intelligence, automatic control engineering, butterfly effect, computer science, cybernetics, robotics.