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A trophic function was first introduced in the differential equations of the Kolmogorov predator–prey model. It generalizes the linear case of predator–prey interaction firstly described by Volterra and Lotka in the Lotka–Volterra equation. A trophic function represents the consumption of prey assuming a given number of predators. The trophic function (also referred to as the functional response) was widely applied in chemical kinetics, biophysics, mathematical physics and economics. In economics, "predator" and "prey" become various economic parameters such as prices and outputs of goods in various linked sectors such as processing and supply. These relationships, in turn, were found to behave similarly to the magnitudes in chemical kinetics, where the molecular analogues of predators and prey react chemically with each other.
These inter-disciplinary findings suggest the universal character of trophic functions and the predator–prey models in which they appear. They give general principles for the dynamic interactions of objects of different natures, so that the mathematical models worked out in one science may be applied to another. Trophic functions have proven useful in forecasting temporarily[clarification needed] stable conditions (limit cycles and/or attractors) of the coupled dynamics of predator and prey. The Pontryagin L.S. theorem[clarification needed] on the inflection points of trophic functions guarantees the existence of a limit cycle in these systems.
Trophic functions are especially important in situations of chaos, when one has numerous interacting magnitudes and objects, as is particularly true in global economics. To define and forecast the dynamics in this case is scarcely possible with linear methods, but non-linear dynamic analysis involving trophic functions leads to the discovery of limit cycles or attractors. Since in nature there exist only temporarily stable objects, such limit cycles and attractors must exist in the dynamics of observed natural objects (chemistry, flora and fauna, economics, cosmology). The general theory suggests as-yet-unknown regularities in the dynamics of the various systems surrounding us.
Despite the success already achieved in research on trophic functions, the field still has great further theoretical potential and practical importance. Global economics, for instance, needs tools to forecast the dynamics of outputs and prices over a scale of at least 3–5 years so as to maintain stable demand and not over-produce, and to prevent crises such as that of 2008.
A trophicfunction was first introduced in the differential equations of the Kolmogorov predator–prey model. It generalizes the linear case of predator–prey...
Look up trophic in Wiktionary, the free dictionary. The trophic level of an organism is the position it occupies in a food web. Within a food web, a food...
called trophic links. The number of trophic links per consumer is a measure of food web connectance. Food chains are nested within the trophic links of...
plant growth, followed by corollary increases in subsequent trophic levels. Consequently, trophic index may sometimes be used to make a rough estimate of...
cells. Trophic hormones can be found in body systems including the endocrine, gastrointestinal, urinary, and nervous systems. The term trophic is from...
Trophic coherence is a property of directed graphs (or directed networks). It is based on the concept of trophic levels used mainly in ecology, but which...
bioproductivity at each trophic level in an ecosystem. A pyramid of energy shows how much energy is retained in the form of new biomass from each trophic level, while...
eggs. In most species that produce them, a trophic egg is usually an unfertilised egg. The production of trophic eggs has been observed in a highly diverse...
Apex predators are usually defined in terms of trophic dynamics, meaning that they occupy the highest trophic levels. Food chains are often far shorter on...
Trophic cascades are powerful indirect interactions that can control entire ecosystems, occurring when a trophic level in a food web is suppressed. For...
heart and posited the idea of nerves and the basic principles on the trophicfunction of the nervous system. Additionally, his collaboration with the Botkin...
they consume for energy in trophic levels, and they are most commonly quantified in length-the number of links between a trophic consumer and the base of...
clearance of apoptotic cells, are being increasingly recognized for their trophicfunction and role in regeneration. Newton PM, Watson JA, Wolowacz RG, Wood EJ...
clearance of apoptotic cells, are being increasingly recognized for their trophicfunction and role in regeneration. Mills CD (2012). "M1 and M2 Macrophages:...
they are said to have a trophic level of 1 (from the Greek trophē meaning food). Phytoplankton are then consumed at the next trophic level in the food chain...
one trophic level. Carnivores may capture some prey that is part of a plant-based trophic system and others that are part of a detritus-based trophic system...
that maintain an organ or body part are said to have trophic effects. A diminished muscular trophic condition is designated as atrophy. Atrophy is reduction...
trophic levels. The trophic level of a fish is the position it occupies on the food chain. The article establishes the importance of the mean trophic...
photosynthesis is carried through the trophic levels of an ecosystem as organisms consume members of lower trophic levels. Primary production can be broken...
Questionnaire, physical examination (sensory function, motor function, pain, electrodiagnostic, trophicfunction), and patient self-assessments. One study...
Trophic species are a scientific grouping of organisms according to their shared trophic (feeding) positions in a food web or food chain. Trophic species...
productivity (production of biomass), decomposition, and trophic interactions. Studies of ecosystem function have greatly improved human understanding of sustainable...
describes the phenomenon of trophic cascade in specific terrestrial communities. A mesopredator is a medium-sized, middle trophic level predator, which both...
founded his own laboratory, which research goal was the adaptation-trophicfunction of the nervous system. 1968 got the academic degree of the Doctor of...
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