A population balance system and method based on Taylor expansion optimization

A population and balanced technology, applied in the biological field, can solve problems such as insufficient correctness of solution verification

Active Publication Date: 2022-05-31
HANGZHOU DIANZI UNIV
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Problems solved by technology

However, the existing technology has deficiencies in solving the ecological balance of the host and verifying the correctness

Method used

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  • A population balance system and method based on Taylor expansion optimization
  • A population balance system and method based on Taylor expansion optimization
  • A population balance system and method based on Taylor expansion optimization

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Embodiment Construction

[0100] The objects and advantages of the present invention will be more apparent through the detailed description of the following population change diagrams in conjunction with the accompanying drawings. In the drawing, the parameter θ=0.65.

[0101] like Figure 1-3 As shown in the present embodiment, a population balance method based on Taylor expansion optimization, the specific steps are as follows:

[0102] Step 1, select the functional response function and establish a mathematical model; specifically, mathematical modeling: in this mathematical model, the host is the victim and the parasite is the beneficiary, so the general host-parasitic model is formulated as:

[0103]

[0104] where X n is the population size of the nth generation host, Y n is the population size of the nth generation parasite, λ is the birth rate of the host (λ>1), That is, the probability of the host escaping the parasite. Substitute the functional response function into equation (2.1) t...

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Abstract

The invention discloses a population balance system and method based on Taylor expansion optimization. The specific steps of the method of the invention are as follows: step 1, select a functional response function, and establish a mathematical model; step 2, solve the balance point of the host and parasite species models; Step 3, draw a circle with the equilibrium point as the center, and obtain the Taylor expansion; Step 4, solve the radius of the circle and conduct analysis and optimization; Step 5, obtain the area of ​​species balance through the local asymptotic stability theorem. Based on the negative binomial distribution relationship between the host and the parasite, the present invention establishes a mathematical model related to the population quantity, uses Taylor expansion optimization and local asymptotic stability methods, and solves the range of the host-parasite population tending towards ecological balance , and the correctness of the method is verified by numerical calculation.

Description

technical field [0001] The invention belongs to the field of biotechnology, and relates to a technical solution for estimating the number of host-parasite populations. Specifically, through Taylor expansion optimization, the local asymptotic stability theorem is used to solve the range in which the population tends to ecological balance, and then the numerical value The calculation verifies the correctness of the method. Background technique [0002] The interaction between animal populations is the main factor affecting the development of ecosystems. In ecological mathematics, models of single populations have been extensively studied, and models of interspecific interactions have yet to be explored, mainly including Lotka-Volterra (Lotka-Volterra) interspecific competition and Nicholson Bailey (Nicholson-Bailey) model of interspecies parasitism. Because the population changes of the Nicholson-Bailey model are unstable, any deviation of any one factor will cause the entir...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F30/27G06N3/00G06F111/10
CPCG06F30/27G06N3/006G06F2111/10
Inventor 何美霖朱铭觉滕旭阳胡志蕊卢从慧
Owner HANGZHOU DIANZI UNIV
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