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Nonlinear Dynamics, An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems is a monthly peer-reviewed scientific journal covering all nonlinear dynamic phenomena associated with mechanical, structural, civil, aeronautical, ocean, electrical, and control systems.
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.
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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Sparse identification of nonlinear dynamics (SINDy) is a data-driven algorithm for obtaining dynamical systems from data. [1] Given a series of snapshots of a dynamical system and its corresponding time derivatives, SINDy performs a sparsity-promoting regression (such as LASSO) on a library of nonlinear candidate functions of the snapshots against the derivatives to find the governing equations.
Nonlinear control theory is the area of control theory which deals with systems that are nonlinear, time-variant, or both. Control theory is an interdisciplinary branch of engineering and mathematics that is concerned with the behavior of dynamical systems with inputs, and how to modify the output by changes in the input using feedback ...