Nonadditive
Definition
Nonadditive, also referred to as nonlinear or non-additive, is a mathematical term used to describe a system which does not respond in a linear fashion to changes in its components. Nonadditivity is most commonly used in the context of nonlinear systems, which typically have a range of behaviors that cannot be predicted using only linear equations.
History
The concept of nonadditivity has its roots in classical mechanics, where the behavior of a system is often described using linear equations. In the 18th century, French mathematician Pierre-Simon Laplace developed the theory of nonlinear systems, which is credited with laying the foundation for modern nonlinear dynamics. The theory was further developed in the 19th century by German mathematician Carl Friedrich Gauss, who introduced the notion of nonadditive systems.
Characteristics
Nonadditive systems are characterized by the fact that changes in one of their components can have a nonlinear impact on the overall behavior of the system. Nonadditive systems are also characterized by a lack of linearity between inputs and outputs, as well as the presence of nonlinear relationships between the components of the system. In addition, nonadditive systems are often characterized by the presence of nonlinear feedback loops, which can lead to complex behavior.
References
Gauss, C. F. (1809). Theoria motus corporum coelestium. Königsberg.
Laplace, P. S. (1799). Exposition du système du monde. Paris.
Chaos Theory: Nonlinear Dynamics for Beginners. (n.d.). Retrieved June 1, 2021, from http://www.scholarpedia.org/article/Chaos_theory
Strogatz, S. H. (1994). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Addison-Wesley.
Dewar, R. (2001). Nonlinear dynamics in engineering systems. Cambridge University Press.