宝鸡文理学院数学与信息科学学院,陕西 宝鸡 721013
李海侠(1977年生),女;研究方向:偏微分方程应用及其可视化;E-mail:xiami0820@163.com
纸质出版日期:2021-05-25,
网络出版日期:2021-01-08,
收稿日期:2019-09-23,
录用日期:2020-09-18
扫 描 看 全 文
李海侠.一类具有毒素的非均匀chemostat模型正解的存在性和稳定性[J].中山大学学报(自然科学版),2021,60(03):167-173.
LI Haixia.Existence and stability of positive solutions for an unstirred chemostat model with toxins[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2021,60(03):167-173.
李海侠.一类具有毒素的非均匀chemostat模型正解的存在性和稳定性[J].中山大学学报(自然科学版),2021,60(03):167-173. DOI: 10.13471/j.cnki.acta.snus.2019.09.23.2019A073.
LI Haixia.Existence and stability of positive solutions for an unstirred chemostat model with toxins[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2021,60(03):167-173. DOI: 10.13471/j.cnki.acta.snus.2019.09.23.2019A073.
研究了一类具有毒素的非均匀chemostat食物链模型。利用最大值原理和上下解方法给出了正解的先验估计。接着运用简单特征值的分歧理论探讨了正解的全局分支,得到了正解存在的充要条件。最后采用线性算子的扰动理论和分歧解的稳定性理论讨论了正分歧解的稳定性。研究结果表明在毒素的影响和适当条件下物种能够共存且正解稳定。
A food chain unstirred chemostat model with toxins is investigated. A priori estimate of positive solutions is given by the maximum principle and the super and sub-solution method. Then by using the bifurcation theory of simple eigenvalues, the global branch of positive solutions is studied, and the sufficient and necessary conditions for the existence of positive solutions are obtained. Finally, the stability of positive bifurcating solutions is discussed by means of the perturbation theory of linear operators and the stability theory of bifurcation solutions. The research results indicate that the species can coexist and positive solutions are stable under the influence of toxins and appropriate conditions.
非均匀chemostat模型分歧理论全局分支稳定性
unstirred chemostat modelbifurcation theoryglobal branchstability
HSU S B, WALTMAN P. On a system of reaction-diffusion equations arising from competition in an unstirred chemostat [J]. SIAM Journal on Applied Mathematics, 1993, 53: 1026-1044.
WU J H. Global bifurcation of coexistence state for the competition model in the chemostat [J]. Nonlinear Analysis, 2000, 39: 817-835.
HSU S B, WALTMAN P. A model of the effect of anti-competitor toxins on plasmid-bearing, plasmid-free competition [J]. Taiwanese J Math, 2002, 6: 135-155.
WU J H, NIE H, WOLKOWICZ G. A mathematical model of competition for two essential resources in the unstirred chemostat[J]. SIAM Journal Applied Mathematics, 2004, 65: 209-229.
ZHU L M, HUANG X C, SU H Q. Bifurcation for a functional yield chemostat when one competitor produces a toxin [J]. J Math Anal Appl, 2007, 329: 891-903.
ZHENG S N, GUO H J, LIU J. A food chain model for two resources in unstirred chemostat [J]. Appl Math Comput, 2008, 206: 389-402.
李艳玲, 李海侠, 吴建华. 一类非均匀Chemostat模型的共存态[J]. 数学学报, 2009, 52(1): 141-152.
LI Y L, LI H X, WU J H. Coexistence states of the unstirred Chemostat model [J]. Acta Mathematica Sinica, 2009, 52(1): 141-152.
WANG Y F, YIN J X. Global dynamics of the periodic un-stirred chemostat with a toxin-producing competitor [J]. Commun Pure Appl Anal, 2010, 9: 1639-1651.
王利娟, 姜洪领. 非均匀Chemostat竞争模型的周期解[J]. 中山大学学报(自然科学版),2010, 49(3): 12-17.
WANG L J, JIANG H L. Periodic solution for the competition model in the unstirred Chemostat [J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2010, 49(3): 12-17.
姜洪领, 王利娟. 一类无搅拌Chemostat模型平衡态正解存在性与数值模拟[J].中山大学学报(自然科学版),2011, 50(3):11-16.
JIANG H L, WANG L J. Existences and numerical simulation of positive solution for a class of unstirred Chemostat model [J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2011, 50(3): 11-16.
NIE H, WU J H. The effect of toxins on the plasmid-bearing and plasmid-free model in the unstirred chemostat [J]. Discrete and Continuous Dynamical Systems, 2012, 32(1): 303-329.
NIE H, WU J H. Multiplicity results for the unstirred chemostat model with general response functions [J]. Science in China: A, 2013, 56: 2035-2050.
NIE H, LIU N, WU J H. Coexistence solutions and their stability of an unstirred chemostat model with toxins [J]. Nonlinear Analysis: Real World Applications, 2014, 20: 36-51.
李海侠. 一类带B-D反应项的非均匀Chemostat模型正解的存在性和多解性[J]. 工程数学学报, 2015, 32(3): 369-380.
LI H X. Existence and multiplicity of positive solutions for an unstirred chemostat model with B-D functional response [J]. Chinese Journal of Engineering Mathematics, 2015, 32(3): 369-380.
贾婷婷, 聂华, 张瑜. 一类具有外加毒素的非均匀恒化器模型分析[J]. 应用数学学报, 2017, 40(3): 377-399.
JIA T T, NIE H, ZHANG Y. The analysis of the unstirred chemostat model with external toxin [J]. Acta Mathematicae Applicatae Sinica, 2017, 40(3): 377-399.
LI H X, WU J H, LI Y L, et al. Positive solutions to the unstirred chemostat model with Crowley-Martin functional response [J]. Discrete and Continuous Dynamical Systems Series B, 2018, 23(8): 2951-2966.
NIE H, HSU S B, WANG F B. Steady-state solutions of a reaction-diffusion system arising from intraguild predation and internal storage [J]. Journal of Differential Equations, 2019, 266(12): 8459-8491.
BELGACEM F. Elliptic boundary value problems with indefinite weights: variational formulations of the principal eigenvalue and applications [M]. Harlow:Addison-Wesley Longman, 1997.
CRANDALL M G, RABINOWITZ P H. Bifurcation from simple eigenvalue [J]. Journal of Functional Analysis, 1971, 8: 321-340.
RABINOWITZ P H. Some global results for nonlinear eigenvalue problems [J]. Journal of Functional Analysis, 1971, 7(3): 487-513.
CRANDALL M G, RABINOWITZ P H. Bifurcation, perturbation of simple eigenvalues and linearized stability [J]. Arch Rational Mech Anal, 1973, 52(2): 161-180.
0
浏览量
0
下载量
0
CSCD
关联资源
相关文章
相关作者
相关机构