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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 ...
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]
Although a unified theory of reaction time and intelligence has yet to achieve consensus among psychologists, diffusion modeling provides one promising theoretical model. Diffusion modeling partitions RT into residual "non-decision" and stochastic "diffusion" stages, the latter of which represents the generation of a decision in a two-choice task.
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 ...
In particular the theory of random graphs has been used as a justification for self-organization as a general principle of complex systems. In the field of multi-agent systems , understanding how to engineer systems that are capable of presenting self-organized behavior is an active research area. [ 45 ]
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]
After more formal works such as Chaos und Struktur (chaos and structure, 1992) or Systemtheorie für Psychotherapeuten, Psychologen und Mediziner (systems theory for psychotherapists, psychologists and physicians, 1999), Kriz has in recent years mostly refrained from explicit formal derivations of the fundamentals in order to address a larger ...