具有Ⅱ类功能性反应的蛛网经济模型研究  

Study on the Cobweb Economic Model with TypeⅡFunctional Response

作　　者：高德宝[1] GAO De-bao(College of Science,Heilongjiang Bayi Agricultural University,Daqing 163319,China)

机构地区：[1]黑龙江八一农垦大学理学院,黑龙江大庆163319

出　　处：《数学的实践与认识》2020年第15期133-142,共10页Mathematics in Practice and Theory

基　　金：黑龙江省哲学社会科学规划项目(19SHE281)。

摘　　要：基于单一商品数量与其价格之间的互动关系构建了蛛网经济微分动力学模型,分析了该模型平衡点的稳定性,给出了其极限环存在的充分条件.在脉冲扰动的条件下,构建了脉冲时刻固定和状态自治的两个蛛网经济模型,探索了前者边界周期解的全局渐近稳定性,研究了后者半平凡周期解的稳定性.最后用数值模拟验证了相关结论的正确性.Based on the interactive relationship between the quantity of the single commodity and its price,the cobweb economic differential dynamics model is constructed.The stability of the equilibrium points of the model are analyzed,and the sufficient condition for the existence of the limit cycle is given.Under the condition of the impulsive perturbation,two cobweb economic models with fixed pulse state and state autonomy are constructed.The global asymptotic stability of the boundary periodic solution of the former is explored.The stability of the semi-trivial periodic solution of the latter is studied.Finally,numerical simulations are used to verify the correctness of the relevant conclusions.

关 键 词：蛛网模型 稳定性 极限环 周期解 数值模拟 

分 类 号：F224[经济管理—国民经济] O175[理学—数学]