基于恐慌情绪的竞争合作交替下的阶段结构切换模型  

A Stage-Structured Switching Model under the Alternation of Competition and Cooperation Based on Panic

作　　者：吕荣健 李华 孙秋柏[2] 李博文 Li Rong-jian;LI Hua;SUN Qiu-bai;LI Bo-wen(School of Electronics and Information Engineering,University of Science and Technology Liaoning,Anshan 114051,China;School of Business Administration,University of Science and Technology Liaoning,Anshan 114051,China)

机构地区：[1]辽宁科技大学电子与信息工程学院,辽宁鞍山114051 [2]辽宁科技大学工商管理学院,辽宁鞍山114051

出　　处：《数学的实践与认识》2023年第12期123-134,共12页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71771112);辽宁社科联项目(L20BGL047)。

摘　　要：提出基于恐慌情绪的竞争合作交替下的阶段结构切换模型.根据竞争与合作将模型分为两个阶段:在第一阶段,用比率依赖型的函数来表示官方舆论场与恐慌竞争的交互作用;在第二阶段,用传染病模型中的双线性关系函数来表示民间舆论场与恐慌合作的交互作用.在恐慌传播的演变过程中,假设每个阶段的周期时间是相同的.这两个阶段通过每个过程的终端时刻连接且切换.证明模型有界性、持久性和灭绝性.数值模拟验证理论结果,描述了突发事件下恐慌情绪传播的规律,并说明交互系数这一参数对模型动力学的影响.本文的研究为政府在应对突发事件时能够及时做出有效决策提供理论依据.In this paper,a stage-structured switching model under the alternation of competition and cooperation based on panic is formulated.The model is divided into two stages according to alternation of competition and cooperation:in the first stage,the ratio-dependent type of functional response is used to represent the competitive interaction between the official opinion field and panic;in the second stage,a bilinear relationship function in the epidemic model is used to represent the cooperative interaction between the public opinion field and panic.In the evolution of panic spread,it is assumed that each stage period time is the same.The two stages are connected and switched by the terminal moments of each process.Boundedness,permanence and extinction of the proposed model is proved.Numerical simulations are given to verify the theoretical results,describe the law of panic spread under emergencies and illustrate the effect of the interaction coefficient parameter on the model dynamics.The research in this paper provides theoretical guidance for the government to make timely and effective decisions in response to emergencies.

关 键 词：阶段结构切换模型 竞争与合作 交互作用 

分 类 号：B842.6[哲学宗教—基础心理学] O175[哲学宗教—心理学]