Predator
The term predator can be defined in two slightly different ways, but in general it can be referred to as a living organism whose survival depends on the killing of another living organism due to its consumption. We refer to the target of predator food as prey.
Definition
From an ecological point of view, a predator can be taken
in the narrower sense as the top link in the grazingprey food chain. So it is always strictly a carnivorous (or omnivorous) species living a predatory way of life. This means that he obtains food, which is always of animal origin, either by actively hunting for prey or by passively waiting for the prey to come on its own. Examples are, for example, the jaguar, the killer whale, the hawk, the moth, and the omnivores, for example, the bear. The exclusion of an entire individual from a population is called true predation. True predation also involves eating seeds and eggs, as seeds and eggs are potential organisms. Thus, an example of true predation also includes such animals as nacre, anteater and even domestic fowl. Note: The difference between true predation  eating seeds  and grazing is that when grazing plants, the whole plant is not consumed, but only a part of it. . In addition, plants are adapted to regenerate lost parts of their body.
Predatorprey mathematical models
The dependence of the amount of prey on the amount of predator can be summarized as follows:
The more prey, the more predatory the predator. A larger number of predators will increase the pressure on the prey, and it will begin to decrease. Eventually, as the amount of prey decreases, so does the amount of predator that is losing food. As the number of predators decreases, the prey's decline stops and its number begins to rise again.
Classical oscillations of predators and prey have been described in nature mainly in cases where the predator has only one predominant prey: ie mainly wolf + white hare and polar fox + lemur in the polar regions. The length of the oscillation varies between 6 and 10 years depending on the environmental conditions.
General mathematical model:
dx / dt x * f (x)

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g (x, y) * y
dy / dt h (x, y) * y

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d * yExplanations:
x  amount of prey
y  amount of predator
f (x)  prey population growth dynamics (see population dynamics) without the presence of a predator
g (x, y)  functional response
h (x, y)  numerical response, mostly ktimes the functional response (expresses the efficiency of conversion of prey biomass to predator biomass)

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d * y  exponential extinction of the predator population (it would happen if prey was not present  the previous term would be zero) Functional response g (x, y)  dependence of the number of eaten individuals on the prey supply x:
LotkaVolterian relation  linear dependence g (x, y) ax, the more prey, the more it is eaten (without restrictions)  in practice it does not exist, it is only an idealized relation.
Holing I  modified LotkaVolterian relation with maximum limit, ie linear relation up to the degree of maximum saturation g (x, y) ax for ax
S  works e.g. for plankton filters.
Holing II  the more the predator is saturated, the less willing he is to look for his prey, the function grows to the limit of the maximum saturation, ie.
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