In dynamical terms, such as in the study of chaos, a non-linear situtation is one where the result is not proportional to the cause. For instance "the straw that broke the camel's back" (eg. the elastic/plastic limit in building structures) introduces non-linearity. Up until that point, deformation had been proportional to load. Suddenly it loses all proportionality.
" Sensitivity to initial conditions" is an indication of the non-linearity of chaotic dynamical systems, where the most minor difference in starting conditions can lead to vast differences in subsequent conditions.
In the study of A-life non-linearity is used to describe systems that do not obey the superposition principle. They are not the sum of their parts. The parts of linear systems can be analysed in isolation and can be combined to understand the system as a whole. The key feature of non-linear systems is that their primary behaviours of interest are properties of the interactions between parts rather than being properties of the parts themselves, and these interactions necessarily disappear when the parts are studied independently. (cf organism)(see also Holland, who also uses the term "epistatic" see below) There are very important feedback mechanisms between levels in such interactions. The interactions among low-level entities give rise to the global level dynamics, which, in turn, affects the lower levels by setting the local context within which each entity's rules are invoked. For Langton, analytic methods work for linear systems, but non-linear systems must be explored through synthetic methods. (see Langton, "Artificial Life")
The effects of different enzymes in the cell are not additive. This phenomenon is known as epistasis. The effect of each allele of a gene depends strongly on what other alleles are present, and there is no simple way to apportion credit to individual alleles for the performance of the resulting phenotype.
When cultural or literary critics use the term, it relates more to "gardens of forking paths" or networks. Hypertext has been described as nonlinear because various choices are possible at any time.