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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 ...
A stirred BZ reaction mixture showing changes in color over time. The discovery of the phenomenon is credited to Boris Belousov.In 1951, while trying to find the non-organic analog to the Krebs cycle, he noted that in a mix of potassium bromate, cerium(IV) sulfate, malonic acid, and citric acid in dilute sulfuric acid, the ratio of concentration of the cerium(IV) and cerium(III) ions ...
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.
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 theory, which can be called a reaction–diffusion theory of morphogenesis, has become a basic model in theoretical biology. [2] Such patterns have come to be known as Turing patterns . For example, it has been postulated that the protein VEGFC can form Turing patterns to govern the formation of lymphatic vessels in the zebrafish embryo.
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 ...
Possible mechanisms of pattern formation in biological systems include the classical reaction–diffusion model proposed by Alan Turing [10] and the more recently found elastic instability mechanism which is thought to be responsible for the fold patterns on the cerebral cortex of higher animals, among other things. [11] [12]
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.