BOUNDEDNESS AND ASYMPTOTIC STABILITY IN A PREDATOR-PREY CHEMOTAXIS SYSTEM WITH INDIRECT PURSUIT-EVASION DYNAMICS  

作　　者：Shuyan QIU Chunlai MU Hong YI 邱蜀燕;穆春来;易红(School of Sciences,Southwest Petroleum University,Chengdu 610500,China;College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China;School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]School of Sciences,Southwest Petroleum University,Chengdu 610500,China [2]College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China [3]School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China

出　　处：《Acta Mathematica Scientia》2022年第3期1035-1057,共23页数学物理学报（B辑英文版）

基　　金：supported by the Young Scholars Development Fund of SWPU(202199010087);the Scientific Research Starting Project of SWPU(2021QHZ016);supported by the National Natural Science Foundation of China(11771062and 11971082);the Fundamental Research Funds for the Central Universities(2019CDJCYJ001);Chongqing Key Laboratory of Analytic Mathematics and Applications。

摘　　要：This work explores the predator-prey chemotaxis system with two chemicals {u_(t) = Δu + ∇ ・ (u∇v) + μ_(1)u(1 − u − α_(1)w), x ∈ Ω, t > 0,v_(t )= Δv −α_(1)v + β_(1)w, x ∈ Ω, t > 0,w_(t) = Δw − ξ∇ ・ (w∇z) + μ_(2)w(1 + α_(2)u − w), x ∈ Ω, t > 0,z_(t) =Δz −α_(2)z +β_(2)u, x ∈ Ω, t > 0, in an arbitrary smooth bounded domainΩ■R^(n) under homogeneous Neumann boundary conditions.The parameters in the system are positive.We first prove that if n≤3,the corresponding initial-boundary value problem admits a unique global bounded classical solution,under the assumption thatχ,ξ,μ_(i),a_(i),α_(i) andβ_(i)(i=1,2)satisfy some suitable conditions.Subsequently,we also analyse the asymptotic behavior of solutions to the above system and show that·when a_(1)<1 and bothμ1/χ^(2) andμ2/ξ^(2) are sufficiently large,the global solution(u,v,w,z)of this system exponentially converges to(1-a_(1)/1+a_(1)a_(2),β_(1)(1+a_(2))/α_(1)(1+a_(1)a_(2)),1+a_(2)/1+a_(1)a_(2),β_(2)(1-a_(1))/α_(2)(1+a_(1)a_(2)))as t→∞;·when a1>1 andμ_(2)/ξ_(2) is sufficiently large,the global bounded classical solution(u,v,w,z)of this system exponentially converges to(0,α_(1)/β_(1),1,0)as t→∞;·when a1=1 andμ_(2)/ξ_(2) is sufficiently large,the global bounded classical solution(u,v,w,z)of this system polynomially converges to(0,α_(1)/β_(1),1,0)as t→∞.

关 键 词：CHEMOTAXIS PREDATOR-PREY BOUNDEDNESS STABILIZATION 

分 类 号：Q141[生物学—生态学] O175[生物学—普通生物学]