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However, real-world systems are often nonlinear and multidimensional, in some instances rendering explicit equation-based modeling problematic. Empirical models, which infer patterns and associations from the data instead of using hypothesized equations, represent a natural and flexible framework for modeling complex dynamics.
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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]
Dynamical neuroscience describes the non-linear dynamics at many levels of the brain from single neural cells [3] to cognitive processes, sleep states and the behavior of neurons in large-scale neuronal simulation. [4] Neurons have been modeled as nonlinear systems for decades, but dynamical systems are not constrained to neurons.
Nonlinear Dynamics. Models of bifurcation and chaos by Elmer G. Wiens; Sci.Nonlinear FAQ 2.0 (Sept 2003) provides definitions, explanations and resources related to nonlinear science; Online books or lecture notes. Geometrical theory of dynamical systems. Nils Berglund's lecture notes for a course at ETH at the advanced undergraduate level.
The Journal of Computational and Nonlinear Dynamics is a quarterly peer-reviewed multidisciplinary scientific journal covering the study of nonlinear dynamics. It was established in 2006 and is published by the American Society of Mechanical Engineers. The editor-in-chief is Balakumar Balachandran (University of Maryland).
Ali Hasan Nayfeh (Arabic: علي نايفة) (21 December 1933 – 27 March 2017) [1] was a Palestinian-Jordanian mathematician, mechanical engineer and physicist. [2] He is regarded as the most influential scholar and scientist in the area of applied nonlinear dynamics in mechanics and engineering. [3]
The method removes secular terms—terms growing without bound—arising in the straightforward application of perturbation theory to weakly nonlinear problems with finite oscillatory solutions. [1] [2] The method is named after Henri Poincaré, [3] and Anders Lindstedt. [4]