考虑空间扩散的三物种食物链系统的演化模拟研究
Study on Evolution Simulation of Three-Species Food Chain System Considering Spatial Diffusion
DOI: 10.12677/AAM.2019.85112, PDF,    科研立项经费支持
作者: 余玲慧, 彭 妆, 汤璐瑶:南京理工大学理学院,江苏 南京
关键词: 三物种食物链偏微分方程种群演化Three Species Food Chain Partial Differential Equation Population Evolution
摘要: 本文我们将研究三物种组成的食物链模型,考虑各个物种在空间中的随机迁移,建立反应扩散型偏微分方程,通过数值模拟来研究种群的演化,并结合理论分析对种群演化的观测结果进行定性的解释。
Abstract: In this paper, we will study the food chain model of the three species, consider the random migra-tion of each species in space, establish reactive diffusion partial differential equations, and study the evolution of the population through numerical simulation. The qualitative interpretation of the observation results of population evolution is carried out in combination with theoretical analysis.
文章引用:余玲慧, 彭妆, 汤璐瑶. 考虑空间扩散的三物种食物链系统的演化模拟研究[J]. 应用数学进展, 2019, 8(5): 984-989. https://doi.org/10.12677/AAM.2019.85112

参考文献

[1] Lotka, A.J. (1925) Elements of Physiological Biology. Dover Publications, New York.
[2] Volterra, V. (1926) Fluc-tuation in the Abundance of a Species Considered Mathematically. Nature, 118, 558-560. [Google Scholar] [CrossRef
[3] Zhu, H.Q., Wang, M.X. and Lai, P. (2018) General Two-Species Interacting Lotka-Volterra System: Population Dynamics and Wave Propagation. Physical Review E, 97, 052413. [Google Scholar] [CrossRef
[4] Vance, R.R. (1984) The Effect of Dispersal on Population Sta-bility in One-Species, Discrete-Space Population Growth Models. American Naturalist, 123, 230. [Google Scholar] [CrossRef
[5] Allen, L.J.S. (1983) Persistence and Extinction in Lotka-Volterra Reac-tion-Diffusion Equations. Mathematical Biosciences, 65, 1-12. [Google Scholar] [CrossRef
[6] Takeuchi, Y. (1986) Bulletin of Mathematical Biology, Vol. 48, 585.
[7] Hastings, A. (1978) Global Stability in Lotka-Volterra Systems with Diffusion. Journal of Mathematical Biology, 6, 163-168. [Google Scholar] [CrossRef
[8] Wang, M.-X. and Ma, Y.-Q. (2013) Population Evolution in Mutualistic Lotka-Volterra System with Spatial Diffusion. Physica A, 395, 228-235. [Google Scholar] [CrossRef
[9] Wang, M.-X. and Lai, P.-Y. (2012) Population Dynamics and Wave Propagation in a Lotka-Volterra System with Spatial Diffusion. Physical Review E, 86, 051908. [Google Scholar] [CrossRef
[10] Do, Y., Baek, H., Lim, Y. and Lim, D. (2011) A Three-Species Food Chain System with Two Types of Functional Responses. Abstract and Applied Analysis, 2011, Article ID 934569. [Google Scholar] [CrossRef