DYNAMICAL SYSTEM Meaning and
Definition
-
A dynamical system is a mathematical concept that refers to a set of changing quantities over time or a system whose properties change over time. It is often used to study complex systems in physics, mathematics, and other scientific disciplines.
In a dynamical system, the dynamics refer to the rules or equations that determine how the system evolves over time. These rules could be deterministic, meaning that the future behavior of the system is entirely determined by its present state, or they might exhibit some form of randomness or uncertainty.
The quantities or variables that change within a dynamical system are often referred to as state variables, and they describe the state or condition of the system at any given time. These variables can be continuous or discrete depending on the nature of the system being studied.
Dynamical systems can exhibit various types of behavior, such as stability, periodicity, chaos, bifurcation, or attractors. Stability refers to a system that converges to a fixed point or equilibrium over time, while periodicity refers to repeated or periodic behavior. Chaos, on the other hand, refers to highly sensitive or unpredictable behavior, often characterized by extreme dependence on initial conditions. Bifurcation refers to the splitting or branching of a system's behavior, and attractors are points or sets of points towards which a system tends to move in the long run.
The study of dynamical systems involves the analysis of their behavior, often through the use of mathematical methods like differential equations, phase space diagrams, and computer simulations.
Common Misspellings for DYNAMICAL SYSTEM
- synamical system
- xynamical system
- cynamical system
- fynamical system
- rynamical system
- eynamical system
- dtnamical system
- dgnamical system
- dhnamical system
- dunamical system
- d7namical system
- d6namical system
- dybamical system
- dymamical system
- dyjamical system
- dyhamical system
- dynzmical system
- dynsmical system
- dynwmical system
- dynqmical system
Etymology of DYNAMICAL SYSTEM
The term "dynamical system" has its roots in the Greek word "dynamis" (δύναμις), which means "power" or "force". The term "dynamical" refers to the notion of motion, change, or evolution over time.
The concept of dynamical systems emerged in the field of mathematics during the late 19th and early 20th centuries. It was initially used to describe systems of differential equations that represent the evolution of physical phenomena. Over time, the term has been broadly applied to various interdisciplinary fields, including physics, engineering, biology, economics, and more, to study the behavior and evolution of complex systems.
