线性扰动May-Leonard竞争模型的动力学
Dynamics of a linearly-perturbed May-Leonard competition model
AI总结：
本文研究线性扰动May-Leonard竞争模型，发现小突变率下系统保留部分原有动力学并出现新稳定不动点，但破坏异宿连接，线性扰动显著影响系统行为。
摘要：
May-Leonard模型是为了研究三个竞争种群的行为而引入的，其中会出现丰富的动力学现象，如极限环和非周期循环解。在本工作中，我们通过添加全局突变能力来扰动系统，允许一个物种以线性方式演化成另外两个物种。我们发现，对于小的突变率，扰动系统不仅保留了经典模型中的一些动力学特性，例如三个种群等数量平衡点分岔出极限环，而且还表现出新的行为。例如，我们捕捉到了折叠分岔曲线，其中成对的平衡点出现然后合并。因此，我们发现了具有新型稳定不动点的参数区域，这些不动点不同于原始模型特有的单种群和双种群平衡点。相反，线性扰动系统无法维持原始系统中存在的异宿连接。总之，即使突变率很小，线性扰动也足以显著影响动力学。
英文摘要：
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.
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