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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]
These systems are often very difficult to solve, so modeling of networks as a linear dynamical systems is easier. Linear systems contain no products between xs and are always solvable. They have the following form for all i: = + + + Unfortunately, biological systems are often nonlinear and therefore need nonlinear models.
A complex system is a system composed of many components which may interact with each other. [1] Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations (like cities), an ecosystem, a living cell, and, ultimately, for ...
Contrary to phenomenological modelling, nonlinear modelling can be utilized in processes and systems where the theory is deficient or there is a lack of fundamental understanding on the root causes of most crucial factors on system. Phenomenological modelling describes a system in terms of laws of nature.
Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically . Natural patterns include symmetries , trees , spirals , meanders , waves , foams , tessellations , cracks and stripes. [ 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.
Examples of anomalous diffusion in nature have been observed in ultra-cold atoms, [3] harmonic spring-mass systems, [4] scalar mixing in the interstellar medium, [5] telomeres in the nucleus of cells, [6] ion channels in the plasma membrane, [7] colloidal particle in the cytoplasm, [8] [9] [10] moisture transport in cement-based materials, [11 ...
Also, the output of a linear system can contain harmonics (and have a smaller fundamental frequency than the input) even when the input is a sinusoid. For example, consider a system described by () = (+ ()) (). It is linear because it satisfies the superposition principle.