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For example, some aspects of the weather are seen to be chaotic, where simple changes in one part of the system produce complex effects throughout. This nonlinearity is one of the reasons why accurate long-term forecasts are impossible with current technology. Some authors use the term nonlinear science for the study of nonlinear systems. This ...
Other examples of nonlinear functions include exponential functions, logarithmic functions, trigonometric functions, power functions, Gaussian function, and Lorentz distributions. Some functions, such as the exponential or logarithmic functions, can be transformed so that they are linear.
An example of a nonlinear delay differential equation; applications in number theory, distribution of primes, and control theory [5] [6] [7] Chrystal's equation: 1 + + + = Generalization of Clairaut's equation with a singular solution [8] Clairaut's equation: 1
An example of a nonlinear control system is a thermostat-controlled heating system. A building heating system such as a furnace has a nonlinear response to changes in temperature; it is either "on" or "off", it does not have the fine control in response to temperature differences that a proportional (linear) device would have.
One example of nonlinear filters is the (generalized directional distance rational hybrid filter (GDDRHF) [1]) for multidimensional signal processing.This filter is a two-stage type hybrid filter: 1) the stage norm criteria and angular distance criteria to produce three output vectors with respect to the shape models; 2) the stage performs vector rational operation on the above three output ...
Nonlinearity can have several effects, which are unwanted in typical situations. The a 3 {\displaystyle a_{3}} term for example would, when the input is a sine wave with frequency ω {\displaystyle \omega } , result in an extra sine wave at 3 ω {\displaystyle 3\omega } , as shown below.
For example, the method can fail if the system emphasizes higher harmonics of the nonlinearity. Such examples have been presented by Tzypkin for bang–bang systems. [ 4 ] A fairly similar example is a closed-loop oscillator consisting of a non-inverting Schmitt trigger followed by an inverting integrator that feeds back its output to the ...
Name Dim Equation Applications Landau–Lifshitz model: 1+n = + Magnetic field in solids Lin–Tsien equation: 1+2 + = Liouville equation: any + = Liouville–Bratu–Gelfand equation