A system and method for single-species balance based on constructing definite liapunov function

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

Active Publication Date: 2022-05-13
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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  • A system and method for single-species balance based on constructing definite liapunov function
  • A system and method for single-species balance based on constructing definite liapunov function
  • A system and method for single-species balance based on constructing definite 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] like 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 liapunov ...

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Abstract

The invention discloses a single population balance system and method based on constructing a positive Liapunov function. The method of the invention follows the steps: Step 1. Construct a mathematical model of the population; Step 2. Calculate the equilibrium point that the population tends to; Step 3. According to the stability of the equilibrium point, construct the fixed Liapunov function; Step 4. According to the stability of the fixed Liapunov function, analyze and optimize with the equilibrium point as the limit; Step 5. The population density tends to the equilibrium point to obtain the area of ​​species balance . In order to explore the stability of a single species, the present invention constructs a fixed Liapunov function through mathematical modeling of a density-limited single species. According to the global asymptotic stability theorem, the equilibrium point is used as an asymptotic line analysis and optimization to solve the single species The area tends to ecological balance, and then numerical simulation verifies the correctness of the method.

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 Patents(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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