论文标题
线性扰动的May-Leonard竞争模型的动力学
Dynamics of a linearly-perturbed May-Leonard competition model
论文作者
论文摘要
引入了五月 - 皇室模型，以检查三个相互竞争的人群的行为，在这些人群中出现了丰富的动力学，例如极限周期和非周期性循环解决方案。在这项工作中，我们通过添加全局突变的能力来扰动系统，从而使一个物种以线性方式演变为其他两个物种。我们发现，对于小型突变率，扰动系统不仅保留了经典模型中看到的一些动力学，例如三个物种相等的均衡平衡分叉至限制周期，而且还具有新的行为。例如，我们捕获了折叠分叉的曲线，其中成对的平衡出现然后结合。结果，我们以新型的稳定固定点的方式揭示了与原始模型的单人群平衡特征不同的稳定固定点。相反，线性扰动的系统无法维持原始系统中存在的异晶连接。简而言之，线性扰动被证明足够重要，即使突变率较小，也可以实质性地影响动力学。
The May--Leonard model was introduced to examine the behavior of three competing populations where rich dynamics, such as limit cycles and nonperiodic cyclic solutions, arise. In this work, we perturb the system by adding the capability of global mutations, allowing one species to evolve to the other two in a linear manner. We find that for small mutation rates the perturbed system not only retains some of the dynamics seen in the classical model, such as the three-species equal-population equilibrium bifurcating to a limit cycle, but also exhibits new behavior. For instance, we capture curves of fold bifurcations where pairs of equilibria emerge and then coalesce. As a result, we uncover parameter regimes with new types of stable fixed points that are distinct from the single- and dual-population equilibria characteristic of the original model. On the contrary, the linearly-perturbed system fails to maintain heteroclinic connections that exist in the original system. In short, a linear perturbation proves to be significant enough to substantially influence the dynamics, even with small mutation rates.
