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首页> 外文期刊>Applied Mathematical Modelling >Stability and Hopf-bifurcation in a general Gauss type two-prey and one-predator system
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Stability and Hopf-bifurcation in a general Gauss type two-prey and one-predator system

机译：一类高斯型两食饵一捕食者系统的稳定性和Hopf分支。

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摘要

A Gauss type general prey-predator mathematical model is proposed and analysed to study the effect of predation on two competing prey species. The growth rate and functional responses are taken to be general non-linear functions. By analysing the model, local stability of all possible equilibrium points is discussed. By choosing a suitable Lyapunov function the global stability of the system at positive equilibrium point is also found. For the purpose of numerical simulation, growth rates of both prey species are taken to be logistic and the predator's functional response on the prey species are taken as Holling type-Ⅱ. Taking death rate of the predator as a bifurcation parameter, we observe Hopf-bifurcation of the system. Then we have discussed the stability and direction of the Hopf-bifurcation. We also observed that intra-specific interference factor is an important parameter in governing the dynamics of the system.
机译：提出并分析了高斯型广义捕食者数学模型，研究了捕食对两个竞争性捕食物种的影响。增长率和功能响应被认为是一般的非线性函数。通过分析模型，讨论了所有可能平衡点的局部稳定性。通过选择合适的李雅普诺夫函数，还可以找到系统在正平衡点的整体稳定性。出于数值模拟的目的，将两种猎物的生长速度视为对数，并将捕食者对猎物的功能响应视为HollingⅡ型。以捕食者的死亡率为分叉参数，我们观察了系统的Hopf分叉。然后，我们讨论了Hopf分支的稳定性和方向。我们还观察到种内干扰因子是控制系统动力学的重要参数。

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  • 来源
    《Applied Mathematical Modelling》 |2016年第12期|5793-5818|共26页
  • 作者

    B.D. Deka; Atasi Patra; Jai Tushar; B. Dubey;

  • 作者单位

    Department of Mathematics, Darrang College, Tezpur-784001, India;

    Department of Mathematics, Birla Institute of Technology and Science, Pilani-333031, India;

    Department of Mathematics, Birla Institute of Technology and Science, Pilani-333031, India;

    Department of Mathematics, Birla Institute of Technology and Science, Pilani-333031, India;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Stability; Prey-predator system; Hopf-bifurcation; Limit cycle;

    机译：稳定性;捕食系统Hopf分支极限循环;

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