JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (1): 81-87.doi: 10.6040/j.issn.1671-9352.0.2016.314
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WANG Shuang-ming
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| [1] CAPASSO V. Mathematical structures of epidemic systems(lecture notes in biomath)[M]. Heidelberg: Springer-Verlag, 1993: 59-75. [2] KUANG Yang. Delay differential equations with applications in population dynamics[M]. Boston: Academic Press, 1993: 119-143. [3] SMITH H L. Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. Mathematical surveys and monographs[M]. Providence: American Mathematical Society, 1995: 145-161. [4] SMOLLER J. Shock waves and reaction-diffusiom equations[M]. Berlin: Springer-Verlag, 1983: 181-198. [5] 王智诚, 王双明. 一类时间周期的时滞反应扩散模型的空间动力学研究[J]. 兰州大学学报(自然科学版), 2013(4): 535-540. WANG Zhicheng, WANG Shuangming. Spatial dynamics of a class of delayed nonlocal reaction-diffusion model with time period[J]. Journal of Lanzhou University(Natural Sciences), 2013(4):534-540. [6] ZHAO Xiaoqiang. Dynamical systems in population biology[M]. New York: Springer-Verlag, 2003: 63-98. [7] ZHANG Liang, WANG Zhicheng. Spatial dynamics of a diffusive predator-prey model with stage structure[J]. Discrete Continuous Dynamical Systems Ser B, 2015, 20(6):1831-1853. [8] ZHANG Liang, WANG Zhicheng, ZHAO Xiaoqiang. Threshold dynamics of a time periodic reaction—diffusion epidemic model with latent period[J]. Journal of Differential Equations, 2015, 258(9):3011-3036. [9] CAPASSO V, MADDALENA L. Convergence to equilibrium states for a reaction-diffusion system modelling the spatial spread of a class of bacterial and viral diseases[J]. J Math Biology, 1981, 13(2):173-184. [10] WU Shiliang. Entire solutions in a bistable reaction-diffusion system modeling man-environment-man epidemics[J]. Nonlinear Analysis: Real World Applications, 2012, 13(5):1991-2005. [11] WU Shiliang, WANG Haiyan. Front-like entire solutions for monostable reaction-diffusion systems[J]. Journal of Dynamics and Differential Equations, 2013, 25(2):505-533. [12] YANG Yunrui, LI Wantong, WU Shiliang. Exponential stability of traveling fronts in a diffusion epidemic system with delay[J]. Nonlinear Analysis: Real World Applications, 2011, 12(2):1223-1234. [13] HESS P. Periodic-parabolic boundary value problems and positivity[M]. Harlow, UK: Longman Scientific & Technical, 1991: 30-38. [14] MARTIN R H, SMITH H L. Abstract functional differential equations and Reaction-Diffusion systems[J]. Trans Amer Math Soc, 1990, 321(1):1-44. [15] MARTIN R H. Nonlinear operators and differential equations in banach spaces[M]. New York: John Wiley and Sons, 1976: 354-366. [16] ZHAO Xiaoqiang. Global attractivity and stability in some monotonediscrete dynamical systems[J]. Bull Austral Math Soc, 1996, 53(2):305-324. |
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