论文标题
随机Rosenzweig-Macarthur猎物predator模型的分叉和混乱行为，具有非高斯稳定噪声
Bifurcation and chaotic behaviour in stochastic Rosenzweig-MacArthur prey-predator model with non-Gaussian stable Lévy noise
论文作者
论文摘要
我们对由α稳定运动驱动的随机Rosenzweig-Macarthur模型进行动态分析。我们分析了平衡点的存在，并清楚地说明了它们的稳定性。结果表明，非线性模型最多具有三个平衡点。如果存在共存平衡，则渐近稳定，吸引所有附近的轨迹。绘制相肖像，以获得对猎物predator相互作用的动态基础的有用见解。具体而言，我们提出了一个系统分叉的跨临界分叉曲线。固定概率密度以非本地fokker-Planck方程为特征，并通过一些数值模拟确认。通过应用蒙特卡洛方法并使用统计数据，我们将随着参数的变化绘制大量随机系统的模拟轨迹。对于任意接近原点的初始条件，噪声项的参数变化可能会导致具有变化的未来路径或轨迹，这反映了相互互动的两种特种猎物猎物predenter系统的混乱行为，受到随机影响的影响。
We perform dynamical analysis on a stochastic Rosenzweig-MacArthur model driven by α-stable Lévy motion. We analyze the existence of the equilibrium points, and provide a clear illustration of their stability. It is shown that the nonlinear model has at most three equilibrium points. If the coexistence equilibrium exists, it is asymptotically stable attracting all nearby trajectories. The phase portraits are drawn to gain useful insights into the dynamical underpinnings of prey-predator interaction. Specifically, we present a transcritical bifurcation curve at which system bifurcates. The stationary probability density is characterized by the non-local Fokker-Planck equation and confirmed by some numerical simulations. By applying Monte Carlo method and using statistical data, we plot a substantial number of simulated trajectories for stochastic system as parameter varies. For initial conditions that are arbitrarily close to the origin, parameter changes in noise terms can lead to significantly different future paths or trajectories with variations, which reflect chaotic behaviour in mutualistically interacting two-species prey-predator system subject to stochastic influence.
