参考文献/References:
[1] GILPIN M E,AYALA F J.Global models of growth and competition[J].Proceedings of the National Academy of Sciences,1973,70(12):3590-3593.DOI:10.1073/pnas.70.12.3590.
[2] GILPIN M E,AYALA F J.Schoener’s model and drosophila competition[J].Theoretical Population Biology,1976,9(1):12-14.DOI:10.1016/0040-5809(76)90031-9.
[3] LIU Shengqiang,XIE Xizhuang,TANG Jianliang.Competing population model with nonlinear intraspecific regulation and maturation delays[J].International Journal of Biomathematics,2012,5(3):111-132.DOI:10.1142/S179352 4512600078.
[4] 谢溪庄.具有阶段结构和非局部空间效应的竞争系统的稳定性[J].华侨大学学报(自然科学版),2012,33(6):715-720.DOI:10.11830/issn.1000-5013.2012.06.0715.
[5] MOORE C M,CATELLA S A,ABBOTT K C.Population dynamics of mutualism and intraspecific density dependence: How θ-logistic density dependence affects mutualistic positive feedback[J].Ecological Modelling,2018,368:191-197.DOI:10.1016/j.ecolmodel.2017.11.016.
[6] SETTATI A,HAMDOUNE S,IMLAHI A,et al.Extinction and persistence of a stochastic Gilpin-Ayala model under regime switching on patches[J].Applied Mathematics Letters,2019,90:110-117.DOI:10.1016/j.aml.2018.10.019.
[7] WANG Kai,ZHU Yanling.Asymptotic properties of a stochastic Gilpin-Ayala model under regime switching[J].Nonlinear Analysis: Hybrid Systems,2019,32:79-90.DOI:10.1016/j.nahs.2018.10.011.
[8] SETTATI A,LAHROUZ A.Stability and ergodicity of a stochastic Gilpin-Ayala model under regime switching on patchs[J].International Journal of Biomathematics,2017,10(6):1750090.DOI:10.1142/S1793524517500905.
[9] LU Chun,CHEN Lijuan,WANG Yumin,et al.The threshold of stochastic Gilpin-Ayala model subject to general Lévy jumps[J].Journal of Applied Mathematics and Computing,2019,60:731-747.DOI:10.1007/s12190-018-01234-x.
[10] LIAO Xiaoxin,LI Jia.Stability in Gilpin-Ayala competition models with diffusion[J].Nonlinear Analysis: Theory, Methods and Applications,1997,28(10):1751-1758.DOI:10.1016/0362-546X(95)00242-N.
[11] JIANG Jifa,LIANG Xing,ZHAO Xiaoqiang.Saddle-point behavior for monotone semiflows and reaction-diffusion models[J].J Differential Equations,2004,203(2):313-330.DOI:10.1016/j.jde.2004.05.002.
[12] ZHAO Xiaoqiang.Dynamical systems in population biology[M].2nd ed.New York:Springer,2017.
[13] 叶其孝,李正元,王明新,等.反应扩散方程引论[M].2版.北京:科学出版社,2011.
[14] 林支桂.数学生态学导引[M].北京:科学出版社,2013.
[15] SMITH H L.Monotone dyanmical systems: An introduction to the theory of competitive and cooperative systems[M]//Mathematical Surveys and Monographs.Providence:American Mathematical Society,1995.
[16] KISHIMOTO K,WEINBERGER H.The spatial homogeneity of stable of equilibria of some reaction-diffusion systems on convex domains[J].J Differential Equations,1985,58(1):15-21.DOI:10.1016/0022-0396(85)90020-8.