一类渔业生态扩散系统的动力性分析
The Dynamical Analysis of a Fishery Ecosystem Diffusion Model
摘要:

本文研究一类带有病毒的捕食与被捕食渔业扩散生物经济收获模型，得到了非负平衡点的局部渐近稳定性的一些结果，并且通过构建适当的Lyapunov函数，得到了唯一正平衡点的全局稳定性的充分条件，并通过数值模拟验证了所得到结果的正确性。最后，利用上下解方法，证明了连接两个平衡点的行波解的存在性。

Abstract: In this work, we introduce the bio-economic harvesting of a prey-predator fishery diffusion model with toxicity in which both the species are infected by some toxicants released by some other species. We obtain some results for the locally asymptotical stability of the nonnegative constant equilibria, and the global stability of the unique positive equilibrium is also obtained by constructing suitable Lyapunov function. Numerical simulations are illustrated to confirm our rigorous results. Finally, via the upper and lower solution method, we also show the existence of traveling wave fronts connecting the zero solution with the positive equilibrium of this system.

文章引用：段彩霞, 杜鹏, 廖新元. 一类渔业生态扩散系统的动力性分析[J]. 应用数学进展, 2013, 2(3): 127-134. http://dx.doi.org/10.12677/AAM.2013.23016

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