Dynamical systems theory

Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations.

Description

When differential equations are employed, the theory is called continuous dynamical systems.When difference equations are employed, the theory is called discrete dynamical systems. See Discrete time and continuous time.

When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a cantor set—one gets dynamic equations on time scales (see Time-scale calculus).

Some situations may also be modeled by mixed operators, such as differential-difference equations (see Delay differential equation).

This theory deals with the long-term qualitative behavior of dynamical systems, and studies the nature of, and when possible the solutions of, the equations of motion of systems that are often primarily mechanical or otherwise physical in nature, such as planetary orbits and the behavior of electronic circuits, as well as systems that arise in biology, economics, and elsewhere.

Much of modern research is focused on the study of chaotic systems.

This field of study is also called just dynamical systems, mathematical dynamical systems theory, or the mathematical theory of dynamical systems.

See also

• Baker's map
• Biological applications of bifurcation theory
• Chaos theory
• Combinatorics and dynamical systems
• Complex systems
• Differential equation
• Discrete time and continuous time
• Dynamical system (definition)
• Embodied Embedded Cognition
• Gingerbreadman map
• Halo orbit
• List of dynamical system topics
• List of types of systems theory
• Oscillation
• Postcognitivism
• Recurrence relation
• Recurrent neural network
• Synergetics
• Systemography
• Time-scale calculus

External links

• Dynamical systems theory @ Wikipedia