Population balance system and method based on finite increment theorem

An incremental and theorem technology, applied in the field of biomathematics, can solve problems such as extinction, economic crisis, and ecological environment destruction

Active Publication Date: 2021-07-09
HANGZHOU DIANZI UNIV
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  • Abstract
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  • Application Information

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Problems solved by technology

For example, in Guam in the Pacific Ocean in 2013, due to too many tree snakes, dozen

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  • Population balance system and method based on finite increment theorem
  • Population balance system and method based on finite increment theorem
  • Population balance system and method based on finite increment theorem

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Embodiment Construction

[0112] The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings.

[0113] Such as image 3 As shown, the application scenario of the present invention: in an ecosystem comprising prey and predator populations, its relationship satisfies negative binomial distribution:

[0114]

[0115] Among them, Ψ t and δ t are the populations of the prey and the predator in the tth generation, respectively, and λ is the increment of the prey (λ>1).

[0116] A kind of population balance method based on the finite increment theorem of this embodiment, its specific steps are:

[0117] Step 1, select the functional response function, and establish a mathematical model:

[0118] According to the functional response function, a mathematical model is established:

[0119] Considering that the prey and the predator satisfy the formula (1), let the functional response function Indicates the probability that the pre...

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Abstract

The invention discloses a population balance system and method based on the finite increment theorem; the method comprises the following specific steps: 1, selecting a function reaction function, and building a mathematical model; 2, solving a balance point of the predator and predator species models according to the mathematical model; 3, solving an increment matrix according to the balance point and a finite increment theorem; 4, analyzing the increment matrix through a Liapunov theorem to obtain a population balance area of the predator and the predator. According to the method, the number of predators and the number of predator populations are estimated, the population balance area is solved through the finite increment theorem and the Liapunov theorem, and then the correctness of the method is verified through numerical simulation.

Description

technical field [0001] The invention belongs to the field of biomathematics, and relates to a method for estimating the populations of prey and predators, in particular to a population balance system and method based on the finite increment theorem. Background technique [0002] By establishing mathematical models, the study of ecosystems has become one of the important directions of research. If affected by factors such as food, environment, human activities, etc., the ecosystem will lose its balance. When there are too many predators, the reduction of food will lead to the decline or even extinction of the prey. For example, in Guam in the Pacific Ocean in 2013, due to too many tree snakes, dozens of local birds were greatly reduced or even extinct; would cause an economic crisis. Therefore, in order to protect the ecological environment, quantifying and modeling the population concept and studying the population balance in the ecosystem have potential application value...

Claims

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Application Information

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IPC IPC(8): G06F17/16G06F17/18G06F30/20
CPCG06F17/16G06F17/18G06F30/20
Inventor 何美霖王浩宇王海泉许方敏郑长亮魏超
Owner HANGZHOU DIANZI UNIV
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