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Nonlinearity is a peer-reviewed scientific journal published by IOP Publishing and the London Mathematical Society. The journal publishes papers on nonlinear mathematics, mathematical physics , experimental physics , theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance.
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In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]
Consider a set of data points, (,), (,), …, (,), and a curve (model function) ^ = (,), that in addition to the variable also depends on parameters, = (,, …,), with . It is desired to find the vector of parameters such that the curve fits best the given data in the least squares sense, that is, the sum of squares = = is minimized, where the residuals (in-sample prediction errors) r i are ...
Suppose there are m regression equations = +, =, …,. Here i represents the equation number, r = 1, …, R is the individual observation, and we are taking the transpose of the column vector.
In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations (iterations).
Nonlinear Processes in Geophysics is an open-access peer-reviewed scientific journal publishing research within Earth science. Abstracting and indexing [ edit ]
This agrees with the nonlinear frequency changes found by employing the Lindstedt–Poincaré method. This new solution is valid until = (). Higher-order solutions – using the method of multiple scales – require the introduction of additional slow scales, i.e., t 2 = ε 2 t, t 3 = ε 3 t, etc.