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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]
Linear dynamical systems can be solved exactly, in contrast to most nonlinear ones. Occasionally, a nonlinear system can be solved exactly by a change of variables to a linear system. Moreover, the solutions of (almost) any nonlinear system can be well-approximated by an equivalent linear system near its fixed points. Hence, understanding ...
Various forms of block structured nonlinear models have been introduced or re-introduced. [6] [7] The Hammerstein model consists of a static single valued nonlinear element followed by a linear dynamic element. [8] The Wiener model is the reverse of this combination so that the linear element occurs before the static nonlinear characteristic. [9]
Sinusoidal waves (or linear waves) are waves having equal height and duration during the crest and the trough, and they can be mirrored in both the crest and the trough. Due to Non-linear effects, waves can transform from sinusoidal to a skewed and asymmetric shape.
One currently active field of research is the use of linear optics versus the use of nonlinear optics in quantum computing.For example, one model of linear optical quantum computing, the KLM model, is universal for quantum computing, and another model, the boson sampling-based model, is believed to be non-universal (for quantum computing) yet still seems to be able to solve some problems ...
Even if the plant is linear, a nonlinear controller can often have attractive features such as simpler implementation, faster speed, more accuracy, or reduced control energy, which justify the more difficult design procedure. An example of a nonlinear control system is a thermostat-controlled heating system. A building heating system such as a ...