具有交叉扩散项修正Leslie-Gower捕食模型的全局分歧解  

The global bifurcation solutions of a modified Leslie-Gower predator-prey model with cross-diffusion terms

作　　者：刘梦妍 冯孝周[2] 程丹丹 刘夏 LIU Meng-yan;FENG Xiao-zhou;CHENG Dan-dan;LIU Xia(School of Science,Xi'an Technology University,Xi'an 710032,Shaanxi,China;School of Electronic Information Engineering,Xi'an Technology University,Xi'an 710032,Shaanxi,China)

机构地区：[1]西安工业大学电子信息工程学院,陕西西安710032 [2]西安工业大学基础学院,陕西西安710032

出　　处：《西北师范大学学报(自然科学版)》2025年第2期125-134,共10页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(12326417);国家外国专家项目(G2023041033L);陕西省自然科学基础研究计划项目(2023YBGY016,2023WGZJZD08,2024JCYBMS072);陕西省教育厅科研计划项目(23JSY044);陕西省教育教学改革项目(23BY078);西安工业大学研究生教育改革重点项目(XAGDYJ220106)。

摘　　要：研究一类具有交叉扩散项与Monod-Haldane型功能反应项的捕食-食饵模型在Dirichlet条件下的平衡态局部分歧解与全局分歧解.首先,以食饵的内禀增长率为分歧参数,利用特征值分歧定理证明两个半平凡解邻域的局部分歧解的存在性;其次,利用全局分歧定理将两个局部分歧解延拓为全局分歧解,并利用特征值扰动定理,证明了局部分歧解的稳定性;最后,利用数值模拟方法验证了理论结果的准确性,实现了模型的可视化.结果证明:当参数满足一定条件时,系统的分歧正解存在,即两物种可共存.The local and global bifurcation solutions of a modified Leslie-Gower predator-prey model with cross-diffusion terms and Monod-Haldane functional response terms are studied under Dirichlet condition.Firstly,taking the intrinsic growth rate of prey as the bifurcation parameter,the existence of local bifurcation solutions on two semi-trivial solutions are established by the local bifurcation theorem.Secondly,the two local bifurcation solutions are extended into global bifurcation solutions by the global bifurcation theorem,and then,by the eigenvalue perturbation theorem,the stability of the local bifurcation solution is proved.Finally,the accuracy of the theoretical results and the visualization of the model are discussed by using numerical simulation.The results show that when the parameters meet certain conditions,the bifurcation positive solution of the system exists,that is,the two species can coexist.

关 键 词：捕食-食饵模型 交叉扩散 分歧解 稳定性 数值模拟 

分 类 号：O715.26[理学—晶体学]