具有非局部时滞的反应扩散对流模型的稳定性和Hopf分支OA
Stability and Hopf Bifurcation of a Reaction-Diffusion-Advection Model with Nonlocal Delay
在生态环境中,物种的生存环境往往是不均匀的,且繁殖过程会受到时间滞后的影响.具有时滞和非局部效应的系统可以更精确地模拟种群密度的变化.本文考虑了一个具有非局部延迟和狄利克雷边界条件的反应扩散对流模型.首先,我们研究了模型解的适定性.然后,利用隐函数定理证明了正稳态解的存在性.在得到特征值的一个先验估计的基础上,我们证明了正稳态解的稳定性,并得出了Hopf分支的相关分布.我们的研究表明,非局部和时滞的联合作用对模型的动力学有一定的影响.
In ecological environments,the survival environment of species is often inhomogeneous,and the reproductive process is affected by time delay.System with nonlocal effects and delay can more accurately simulate changes in population density.In this paper,we consider a reaction-diffusion-advection model with nonlocal delay and Dirichlet boundary conditions.First of all,we investigate the well-posedness of solution of model.Then,the existence of positive steady state is proofed by implicit function theorem.Based on a priori estimate for the eigenvalue,we prove the stability of the positive steady state and conclude the associated distribution of Hopf bifurcation.Our research indicates that the combined effects of nonlocal and time delays have a certain impact on the dynamics of the model.
詹纪丹;余锞;彭亚红
东华大学数学与统计学院,上海 201620东华大学数学与统计学院,上海 201620东华大学数学与统计学院,上海 201620
数理科学
非局部性时滞反应扩散对流Hopf分支稳定性
NonlocalityTime delayReaction-diffusion-advectionHopf bifurcationStability
《应用数学》 2026 (2)
373-387,15
Supported by the Natural Science Foundation of Shanghai(23ZR1401700)and National Natural Science Foundation of China(12471157)
评论