鱼群竞争合作动力学模型的稳定性分析

Stability Analysis of a Competition or Cooperation Dynamic Model among Shoal of Fish

摘要: 本文通过对低密度时合作而高密度时竞争的鱼群进行研究，建立了鱼群竞争合作的动力学模型，并结合微分方程稳定性理论，分析了平衡点的稳定性，从而给出鱼群共存的稳定性条件。并在文章最后给出了鱼群演化的生物学解释。

Abstract: To analyze shoal of fish that is cooperation at low density, but is competition at high density, we establish the fish competition or cooperation motivation model. And combining the fish competition or cooperation motivation model, we establish differential equation stability theory, analyze the stability of the equilibrium point, and give two fish coexistence of multiple stability conditions. The shoal evolution of biological explanation is also given eventually.