Single population balance system and method based on construction of definite and positive Liapunov function

A function and population technology, applied in the field of mathematical biology, which can solve problems such as low accuracy

Active Publication Date: 2021-07-16
HANGZHOU DIANZI UNIV
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Problems solved by technology

However, the existing technology has the problem of low accuracy

Method used

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  • Single population balance system and method based on construction of definite and positive Liapunov function
  • Single population balance system and method based on construction of definite and positive Liapunov function
  • Single population balance system and method based on construction of definite and positive Liapunov function

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Embodiment Construction

[0142] The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings.

[0143] Such as Figure 1-4 As shown, this embodiment uses mathematical modeling and uses the global asymptotic stability theorem to calculate the situation that the number of single populations on the plateau tends to ecological balance. The plateau single species model is:

[0144] x t+1 =F(X t )

[0145] where λ is the reproductive rate of the species, a is the reciprocal of the threshold density, and b is the relationship constant between mortality, birth rate and density.

[0146] In order to make the number of plateau single populations tend to ecological balance with the passage of generations, that is, plateau single populations achieve global asymptotic stability, the closed-form expression of the equilibrium point is firstly solved. Then, the fixed Liapunov function is constructed, and the optimization analysis of the liapun...

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Abstract

The invention discloses a single population balance system and method based on construction of a definite and positive Liapunov function. The method comprises the following steps: 1, constructing a mathematical model of a population; 2, calculating a balance point tended by the population; 3, constructing a definite Liapunov function according to the stability of the balance point; 4, according to the stability of the positive Liapunov function, carrying out analysis and optimization by taking a balance point as a limit; and 5, when the population density tends to be a balance point, obtaining a species balance region. In order to explore the stability of the single population, mathematical modeling is carried out on the single population with limited density, a definite and positive Liapunov function is constructed, according to the global asymptotic stability theorem, analysis and optimization are carried out with a balance point as a progressive line, an area where the single population tends to ecological balance is solved, and then the correctness of the method is verified through numerical simulation.

Description

technical field [0001] The invention belongs to the technical field of mathematical biology, and relates to the analysis and research of animal and plant behavior, ecology, social structure, evolutionary process, etc., and specifically relates to a single population balance system and method based on the construction of a fixed Liapunov function. Background technique [0002] By establishing mathematical models, the discipline of studying life phenomena is called mathematical biology, which involves phenomena such as animal and plant behavior, ecology, social structure, and evolutionary process. Observe various phenomena in nature and society, describe their behavior patterns through mathematical models, discover the laws hidden in small changes, analyze the nature of changes, and tap the similarities between different objects. When a species develops unsteadily, it leads to the extinction of the population. For example, if the population density is too high, it will lead t...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F30/27G06N3/00G06F111/10
CPCG06F30/27G06N3/006G06F2111/10
Inventor 何美霖李立辉王海泉胡志蕊滕旭阳宋慧娜
Owner HANGZHOU DIANZI UNIV
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