We consider a population with two equal dominated species, dynamics of which is defined by an one-dimensional piecewise-continuous, two parametric function. It is shown that for any non-zero parameters this function has two fixed points and several periodic points. We prove that all periodic (in particular fixed) points are repelling, and find an invariant set which asymptotically involves the trajectories of any initial point except fixed and periodic ones. We showed that the orbits are unstable and chaotic because Lyapunov exponent is non-negative. The limit sets analyzed by bifurcation diagrams. We give biological interpretations of our results.

中文翻译：

---

具有两个同等优势物种的种群动态

我们考虑具有两个相等的主导物种的种群，其种群动态由一维分段连续的两个参数函数定义。结果表明，对于任何非零参数，此函数都有两个固定点和几个周期点。我们证明所有周期点（特别是固定点）都是排斥的，并找到一个渐近性集合，该集合渐近地涉及任何初始点的轨迹，除了固定点和周期点之外。我们证明了轨道是不稳定且混乱的，因为李雅普诺夫指数是非负的。通过分叉图分析极限集。我们对结果进行生物学解释。