一类具有脉冲控制的互惠扩散模型的动力学分析  

Dynamic analysis of a class of mutualistic diffusive models with impluses control

作　　者：戴青 林支桂[1] DAI Qing;LIN Zhigui(School of Mathematical Science,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《扬州大学学报（自然科学版）》2024年第6期49-55,共7页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(12271470,11911540464).

摘　　要：针对描述两种群互惠模型的反应扩散问题,引入脉冲刻画种群对瞬时干扰的响应过程。结合经典偏微分方程理论和上下解方法,讨论在脉冲影响下反应扩散方程解的性质。结果表明,脉冲和初值对解的爆破都产生影响,较大的脉冲和初值更容易导致爆破现象发生。This paper deals with a reaction-diffusion problem describing two species mutualisticmodeland pulse is introduced to characterize the process of population response toinstantaneousintervention.By combining the classical theory of partial differential equations and the method of upper and lower solutions,the properties of the solution of the reaction-diffusion equation under the influence of the impulse are discussed.Theresultsshow that both impulses and initial values have impacts on blow-up of solutions,and large impulses and initial values are more likely to lead to blowup phenomenon.

关 键 词：互惠模型 脉冲 爆破 上下解方法 

分 类 号：O175.26[理学—数学]