Yonghui ZHOU
,
Yunrui YANG
,
Kepan LIU
. STABILITY OF TRAVELING WAVES IN A POPULATION DYNAMIC MODEL WITH DELAY AND QUIESCENT STAGE[J]. Acta mathematica scientia, Series B, 2018
, 38(3)
: 1001
-1024
.
DOI: 10.1016/S0252-9602(18)30798-7
[1] Aronson D G. The asymptotic speed of propagation of a simple epidemic. Research Notes in Mathematics, 1977, 19(4):1-23
[2] Chen X. Existence, uniqueness and asymptotic stability of traveling waves in nonlocal evolution equations. Adv Differential Equations, 1997, 2:125-160
[3] Fife P C, Mcleod J B. The approach of solutions nonlinear diffusion equations to traveling front soutions. Arch Ration Mech Anal, 1977, 65:335-361
[4] Hadeler K P, Lewis M A. Spatial dynamics of the diffusive logistic equation with a sedentary compartment. Can Appl Math Q, 2002, 10:473-499
[5] Hadeler K P, Hillen, Lewis M A. Biological Modeling with Quiescent Phases. Chapter 5//Cosner C, Cantrell S, Ruan S. Spatial Ecology. Taylor and Francis, 2009
[6] Hale J. Theory of functional differential equation. New York:Springer-Verlag, 1977
[7] Huang R, Mei M, Wang Y. Planar traveling waves for nonlocal dispersal equation with monostable nonlinearity. Disc Conti Dyn Sys, 2012, 32A:3621-3649
[8] Li Y, Li W T, Yang Y R. Stability of traveling waves of a diffusive SIR epidemic model. Journal of Mathematical Physics, 2016, 57(4):041504
[9] Lin C K, Mei M. On traveling wavefronts of Nicholson's blowflies equations with diffusion. Proc R Soc Lond, 2010, 140A:135-152
[10] Lin C K, Lin C T, Lin Y, Mei M. Exponential stability of nonmonotone traveling waves for Nicholson's blowflies equation. SIAM J Math Anal, 2014, 46:1053-1084
[11] Lv G Y, Wang X H. Stability of traveling wave solutions to delayed Evolution Equation. J Dyn Control Syst, 2015, 21:173-187
[12] Mei M, So J W H, Li M Y, Shen S S. Asymptotic stability of traveling waves for the Nicholson's blowflies equation with diffusion. Proc Roy Soc Edinburgh Sect A, 2004, 134:579-594
[13] Mei M, So J W H. Stability of strong traveling waves for a nonlocal time-delayed reaction-diffusion equation. Proc Roy Soc Edinburgh Sect A, 2008, 138:551-568
[14] Mei M, Lin C K, Lin C T, So J W H. Traveling wavefronts for time-delayed reaction-diffusion equation:(I) Local nonlinearity. J Differential Equations, 2009, 247:495-510
[15] Mei M, Lin C K, Lin C T, So J W H. Traveling wavefronts for time-delayed reaction-diffusion equation:(Ⅱ) Nonlocal nonlinearity. J Differential Equations, 2009, 247:511-529
[16] Chern I L, Mei M, Yang X F, Zhang Q F. Stability of non-monotone critical traveling waves for reactiondiffusion equations with time-delay. J Differential Equations, 2015, 259(4):1503-1541
[17] Murray J D. Mathematical Biology. New York:Springer-Verlag, 1989
[18] Wang Z C, Li W T, Ruan S G. Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay. J Differential Equations, 2007, 238:153-200
[19] Wang Z C, Li W T, Ruan S G. Traveling fronts in monostable equations with nonlocal delayed effects. J Dynam Differential Equations, 2008, 20:573-607
[20] Yang Y R, Li W T, Wu S L. Exponential stability of traveling fronts in a diffusion epidemic system with delay. Nonlinear Anal RWA, 2011, 12:1223-1234
[21] Yang Y R, Li W T, Wu S L. Stability of traveling waves in a monostable delayed system without quasimonotoncity. Nonlinear Anal RWA, 2013, 14:1511-1526
[22] Zhang K, Zhao X Q. Asymptotic behavior of a reaction-diffusion model with a quiescent stage. Proc R Soc Lond, 2007, 463A:1029-1043
[23] Zhang P A, Li W T. Monotonicity and uniqueness of traveling waves for a reaction-diffusion model with a quiestent stage. Nonlinear Anal TMA, 2010, 72(5):2178-2189
[24] Zhao H Q, Liu S Y. Spatial dynamics for a non-quasi-monotone reaction-diffusion system with delay and quiescent stage. Appl Math Model, 2016, 40:4291-4301
