JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (10): 122-126.doi: 10.6040/j.issn.1671-9352.0.2023.131

Previous Articles    

Stability of a single population delayed reaction-diffusion model with Dirichlet boundary condition

Yonghua LI(),Cunhua ZHANG   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Received:2023-04-04 Online:2023-10-20 Published:2023-10-17

RichHTML

4

PDF (PC)

248

Abstract:

This paper studies the dynamics of a single population delayed reaction-diffusion model with Dirichlet boundary condition in a bounded domain. The existence and multiplicity of spatially nonhomogeneous steady-state solution is investigated by employing Lyapunov-Schmidt reduction method. Then, the stability of spatially nonhomogeneous steady-state solution is derived by analyzing the distribution of the eigenvalues.

Key words: delayed reaction-diffusion model, Lyapunov-Schmidt reduction, stability

CLC Number: 

  • O175.26
1 DAVIDSON F A , DODDS N . Spectral properties of non-local differential operators[J]. Applicable Analysis, 2006, 85 (6/7): 717- 734.
2 FARIA T . Normal forms for semilinear functional differential equations in Banach spaces and applications[J]. Discrete Contin SIAM Journal on Applied Dynamical Systems, 2001, 7 (1): 155- 176.
doi: 10.3934/dcds.2001.7.155
3 YAN Xiangping , LI Wantong . Stability of bifurcating periodic solutions in a delayed reaction-diffusion population model[J]. Nonlinearity, 2010, 23 (6): 1413- 1431.
doi: 10.1088/0951-7715/23/6/008
4 DENG Yinbin , PENG Shuangjie , YAN Shusen . Positive soliton solutions for generalized quasilinear Schrodinger equations with critical growth[J]. Differential Equations, 2015, 258 (1): 115- 147.
doi: 10.1016/j.jde.2014.09.006
5 YI Fengqi , WEI Junjie , SHI Junping . Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system[J]. Differential Equations, 2009, 246 (5): 1944- 1977.
doi: 10.1016/j.jde.2008.10.024
6 CHEN Shanshan , SHI Junping . Stability and Hopf bifurcation in a diffusive logistic population model with nonlocal delay effect[J]. Differential Equations, 2012, 253 (12): 3440- 3470.
doi: 10.1016/j.jde.2012.08.031
7 GUO Shangjiang . Stability and bifurcation in a reaction-diffusion model with nonlocal delay effect[J]. Differential Equations, 2015, 259 (4): 1409- 1448.
doi: 10.1016/j.jde.2015.03.006
8 SU Ying , WEI Junjie , SHI Junping . Hopf bifurcations in a reaction-diffusion population model with delay effect[J]. Differential Equations, 2009, 247 (4): 1156- 1184.
doi: 10.1016/j.jde.2009.04.017
9 MA Li , WEI Dan . Hopf bifurcation of a delayed reation-diffusion model with advection term[J]. Nonlinear Science, 2021, 212 (2): 112455.
10 GUO Shangjiang , WU Jianhong . Bifurcation theory of functional differential equations[M]. New York: Springer-Verlag, 2013: 41- 58.
11 WU Jianhong . Theory and applications of partial functional-differential equations[M]. New York: Springer-Verlag, 1996: 65- 110.
[1] Zipeng HE,Yaying DONG. Steady-state solutions of a Holling type Ⅱ competition model in heterogeneous environment [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 73-81.
[2] Yadi WANG,Hailong YUAN. Hopf bifurcation analysis in the Lengyel-Epstein reaction diffusion system with time delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 92-103.
[3] Yun NI,Xiping LIU. Existence and Ulam stability for positive solutions of conformable fractional coupled systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 82-91.
[4] HU Yuwen, XU Jiucheng, ZHANG Qianqian. Lyapunov stability of decision evolution set [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(7): 52-59.
[5] LIU Yun, ZHU Pengjun, CHEN Luyao, SONG Kai. Optimization of blockchain sharding by profit incentive algorithm based on edge computing [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(7): 88-96.
[6] HUANG Yu, GAO Guang-hua. Compact difference schemes for the fourth-order parabolic equations with the third Dirichlet boundary [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(4): 16-28.
[7] Gaihui GUO,Jingjing WANG,Wangrui LI. Hopf bifurcation of a vegetation-water reaction-diffusion model with time delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(10): 32-42, 53.
[8] Gang CHEN,Rui ZHANG. Dynamics of a two-strain co-infection epidemic model with vaccination [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(10): 84-96.
[9] Lei LI,Yongsheng YE. Exponential stability of reaction-diffusion Cohen-Grossberg neural networks with Dirichlet boundary conditions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(10): 67-74.
[10] Qian CAO,Yanling LI,Weihua SHAN. Dynamics of a reaction-diffusion predator-prey model incorporating prey refuge and fear effect [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(10): 43-53.
[11] Wenyan LIU,Shuai QIAO,Chenghua GAO. Global dynamics analysis of a class of Filippov-type HR neuron model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(10): 13-23.
[12] LI Xiao-wei, LI Gui-hua. Dynamic behaviors analysis of COVID-19 model with environmental virus effects [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(1): 10-15.
[13] HUO Lin-jie, ZHANG Cun-hua. Stability and Hopf bifurcation of diffusive predator-prey system with Holling-Ⅲ type functional response [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(1): 16-24.
[14] SUN Chun-jie, ZHANG Cun-hua. Stability and Turing instability in the diffusive Beddington-DeAngelis-Tanner predator-prey model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(9): 83-90.
[15] SU Xiao-yan, CHEN Jing-rong, YIN Hui-ling. Generalized interval-valued Pythagorean triangular fuzzy aggregation operator and application in decision making [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(8): 77-87.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] HE Hai-lun， CHEN Xiu-lan* . Circular dichroism detection of the effects of denaturants and buffers on the conformation of cold-adapted protease MCP-01 and  mesophilic protease BP01[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2013, 48(1): 23 -29 .
[2] SUN Xiao-ting1, JIN Lan2*. Application of DOSY in oligosaccharide mixture analysis[J]. J4, 2013, 48(1): 43 -45 .
[3] YANG Ying, JIANG Long*, SUO Xin-li. Choquet integral representation of premium functional and related properties on capacity space[J]. J4, 2013, 48(1): 78 -82 .
[4] Ming-Chit Liu. THE TWO GOLDBACH CONJECTURES[J]. J4, 2013, 48(2): 1 -14 .
[5] ZHAO Tong-xin1, LIU Lin-de1*, ZHANG Li1, PAN Cheng-chen2, JIA Xing-jun1. Pollinators and pollen polymorphism of  Wisteria sinensis (Sims) Sweet[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 1 -5 .
[6] WANG Kai-rong, GAO Pei-ting. Two mixed conjugate gradient methods based on DY[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 16 -23 .
[7] MAO Ai-qin1,2, YANG Ming-jun2, 3, YU Hai-yun2, ZHANG Pin1, PAN Ren-ming1*. Study on thermal decomposition mechanism of  pentafluoroethane fire extinguishing agent[J]. J4, 2013, 48(1): 51 -55 .
[8] LI Yong-ming1, DING Li-wang2. The r-th moment consistency of estimators for a semi-parametric regression model for positively associated errors[J]. J4, 2013, 48(1): 83 -88 .
[9] DONG Li-hong1,2, GUO Shuang-jian1. The fundamental theorem for weak Hopf module in  Yetter-Drinfeld module categories[J]. J4, 2013, 48(2): 20 -22 .
[10] TANG Feng-qin1, BAI Jian-ming2. The precise large deviations for a risk model with extended negatively upper orthant dependent claim  sizes[J]. J4, 2013, 48(1): 100 -106 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd