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Three examples of Turing patterns Six stable states from Turing equations, the last one forms Turing patterns. The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis" which describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state.
Reaction–diffusion systems are naturally applied in chemistry. However, the system can also describe dynamical processes of non-chemical nature. Examples are found in biology, geology and physics (neutron diffusion theory) and ecology. Mathematically, reaction–diffusion systems take the form of semi-linear parabolic partial differential ...
Reaction–diffusion processes form one class of explanation for the embryonic development of animal coats and skin pigmentation. [5] [6] Another reason for the interest in reaction-diffusion systems is that although they represent nonlinear partial differential equations, there are often possibilities for an analytical treatment. [7] [8] [9]
Alan Turing, [17] and later the mathematical biologist James Murray, [83] described a mechanism that spontaneously creates spotted or striped patterns: a reaction–diffusion system. [84] The cells of a young organism have genes that can be switched on by a chemical signal, a morphogen , resulting in the growth of a certain type of structure ...
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 ...
It was named after Richard FitzHugh (1922–2007) [2] who suggested the system in 1961 [3] and Jinichi Nagumo et al. who created the equivalent circuit the following year. [4]In the original papers of FitzHugh, this model was called Bonhoeffer–Van der Pol oscillator (named after Karl-Friedrich Bonhoeffer and Balthasar van der Pol) because it contains the Van der Pol oscillator as a special ...
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]
The Lotka–Volterra system of equations is an example of a Kolmogorov population model (not to be confused with the better known Kolmogorov equations), [2] [3] [4] which is a more general framework that can model the dynamics of ecological systems with predator–prey interactions, competition, disease, and mutualism.