The Dynamical Analysis of a Fishery Ecosystem Diffusion Model
作者: 段彩霞杜鹏廖新元
作者单位: 1南华大学数理学院,衡阳
刊名: Advances in Applied Mathematics, 2013, Vol.02 (03), pp.127-134
中文刊名: 应用数学进展, 2013, Vol.02 (03), pp.127-134
来源数据库: Hans Pubs Journal
DOI: 10.12677/AAM.2013.23016
关键词: Prey-Predator Fishery ModelStabilityLinearized MethodTraveling WavefrontUpper andLower Solution
中文关键词: 捕食与被捕食渔业模型稳定性线性化方法波前解上下解方法
英文摘要: 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.
中文摘要: 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。
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  • Upper 上方
  • Analysis 分析