Global stability of a quasilinear predator-prey model with indirect pursuit-evasion interaction  

作　　者：Chuanjia Wan Pan Zheng Wenhai Shan 

机构地区：[1]School of Science Chongqing University of Posts and Telecommunications Chongqing 400065,P.R.China [2]Department of Mathematics The Chinese University of Hong Kong Shatin,Hong Kong,P.R.China [3]School of Mathematics and Statistics Yunnan University Kunming 650091,P.R.China

出　　处：《International Journal of Biomathematics》2024年第8期147-174,共28页生物数学学报(英文版)

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11601053,12271064);the Science and Technology Research Project of Chongqing Municipal Education Commission(Grant No.KJZD-K202200602);the Natural Science Foundation of Chongqing(Grant No.CSTB2023NSCQ-MSX0099);the Hong Kong Scholars Program(Grant Nos.XJ2021042,2021-005)and the Young Hundred Talents Program of CQUPT in 2022-2024.

摘　　要：This paper deals with a predator-prey model with indirect prey-taxis and predator-taxis{u_(t)=■·(D_(1)(u)■u)-χ■·(S_(1)(u)■z)+u(αv-a_(1)-b_(1)u),x∈Ω,t>0,u_(t)=■·(D_(2)(v)■v)-ε■·(S_(1)(v)■w)+v(a_(2)-b_(2)v),x∈Ω,t>0,0=△ω+βu-γw,x∈Ω,t>0,0=△z+δv-ρz,x∈Ω,t>0,under homogeneous Neumann boundary conditions in a smoothly bounded domainΩblong to R^(n)(n≥1),where the parametersχ,ε,α,β,γ,δ,ρ,a_(1),a_(2),b_(1),b_(2)are positive,D_(1)(u)and D_(2)(v)are nonlinear diffusion functions,Si(u)and S2(v)are nonlinear sensitivity functions.First,under certain suitable conditions for D,and S,with i=1,2,the system admits a unique globally bounded classical solution,provided that b_(1)≥4αand b_(2)>0.Additionally,by constructing appropriate Lyapunov functionals,we investigate the asymptotic stability of the globally bounded solutions and provide the exact convergence rates based on the different parameter choices.

关 键 词：Predator-prey model QUASILINEAR global boundedness STABILIZATION 

分 类 号：O175[理学—数学]