Nonlinearity Guide, Meaning , Facts, Information and Description

A nonlinear system is one that cannot be described by a system of linear equations.

The solutions of linear equations can in general be described as a superposition of other solutions of the same equation. This makes linear equations particularly easy to solve and reason about.

Nonlinear systems are more complex, and much harder to understand because of their lack of simple superposed solutions. In nonlinear systems the solutions to the equations do not form a vector space and cannot be superposed (added together) to produce new solutions. This makes solving the equations much harder than in linear systems.

The necessary mathematical techniques only started to be developed in the 20th century.

= Examples of nonlinear systems =

• general relativity
• the Navier-Stokes equations of fluid dynamics
• systems with solitons as solutions
• nonlinear optics
• the Earth's weather system
• balancing a robot unicycle
• the population cycles of hares and foxes on an island
• economic cycles
• autocatalytic chemical or biochemical reactions
• sexual selection in Darwinian evolution
• The motion of the planets in the solar system
• predator-prey dynamics in ecology
• infectious disease dynamics

= Popular concepts associated with nonlinearity =

• positive feedback
• critical mass
• vicious cycle
• self fulfilling prophecy

See also

• Aleksandr Mikhailovich Lyapunov
• Dynamical system
• linear
• nonlinear medium

External links

• http://www.enm.bris.ac.uk/research/nonlinear/faq-Contents.html
• http://amath.colorado.edu/faculty/jdm/faq.html

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