具有间接信号项扩散的捕食者-食饵模型解的整体有界性  

Global Boundedness of a Diffusive Predator‑Prey Model with Indirect Signal Production

作　　者：王梦琴 吴赛楠 WANG Mengqin;WU Sainan(School of Science,Nanjing University of Posts and Telecommunications,Nanjing 210023,China)

机构地区：[1]南京邮电大学理学院,江苏南京210023

出　　处：《中北大学学报（自然科学版）》2024年第6期791-797,共7页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11901310)。

摘　　要：在空间捕食的活动中,除了捕食者和食饵的随机运动外,还存在着趋化现象。依据生物对化学信号的靠近和远离,可将趋化分为吸引趋化和排斥趋化。本文以捕食者-食饵系统和趋化现象为背景,将食饵分为未受伤食饵和受伤食饵,考虑了一个带有间接信号项扩散的捕食-食饵趋化模型,该模型描述了受伤食饵排出的化学信号物质间接促进了捕食者和未受伤食饵运动的现象,在捕食的过程中,捕食者被受伤的食饵排出的化学信号物质所吸引,而受伤的食饵排出的化学信号物质排斥着未受伤的食饵。通过半群理论以及Moser迭代的方法证明了系统在Neumann边界条件下的有界区域上解的全局存在性和一致有界性。该结果适用于任意趋化敏感系数下的空间维数n≤3的系统。In spatial predator-prey models,in addition to the random diffusion of predator and prey,there is also chemotaxis phenomenon.The cell movement is directed towards the increasing chemical signal concentration,which is called the attractive chemotaxis.And another type chemotaxis model is called repulsive chemotaxis,which indicates that cells move away from the increasing signal concentration.Based on the predator-prey system and chemotaxis system,we considered a diffusive predator-prey model with indirect signal production,where the prey was divided into the uninjured prey and injured prey.This model showed the predator-prey behavior involving the advection effect induced by the chemical signals released by the injured prey,in which the predator was attracted to the chemical excreted by injured prey during the capturing,and which repelled the uninjured prey.The global existence and boundedness of solutions of the system on bounded domains with no-flux boundary condition of Neumann is proved by using the semigroup arguments and Moser-Alikakos iteration,when the arbitrary spatial dimension holds n≤3 and chemotaxis sensitivity coefficients are arbitrary.

关 键 词：捕食者-食饵模型 趋化模型 间接信号 全局有界性 

分 类 号：O141[理学—数学]