基于动态价格下的家畜养殖模型及其分析

Livestock Breeding Model Based on Dynamic Price and Its Analysis

摘要: 在任何生物经济学研究中，市场价格都是最重要的工具之一。养殖户的每一步都取决于其市场价格。羊的市场价格与消费者的需求量，羊的市场供给量有密切的关系。本文以羊养殖为例，以Logistic增长模型为基础，根据市场价格变化对养殖户行为的影响建立了价格影响下的动态单种群养殖模型，利用定性理论证明了平衡点的存在性、局部稳定性、极限环的不存在性、出现的跨临界点分支，利用Poincar-Bendixson准则证明平衡点的全局稳定性。该模型与内蒙古地区每年年底羊的存栏量数据相吻合，通过重要参数变化下的分支现象进行现实解释，可以发现养殖成本、出栏率、市场需求量对当前养殖量的影响，反映了动态价格影响下，养殖量的变化过程，为养殖户的长期决策提供了一定的建议。

Abstract: In any Bioeconomic research, market price is one of the most important tools. Every step of farmers depends on their market price. The market price of sheep is closely related to the demand of con-sumers and the market supply of sheep. Taking sheep breeding as an example, based on the logistic growth model, a dynamic single population breeding model under the influence of market price change on Farmers’ behavior is established. The existence, local stability, nonexistence of limit cycle and cross critical point branches of the equilibrium point are proved by using qualitative theory, and the global stability of the equilibrium point is proved by using Poincar Bendixson criterion. The model is consistent with the data of sheep stock at the end of each year in Inner Mongolia. Through the realistic explanation of the branching phenomenon under the change of important parameters, we can find the impact of breeding cost, marketing rate and market demand on the current breed-ing quantity, reflect the change process of breeding quantity under the influence of dynamic price, and provide some suggestions for farmers’ long-term decision-making.