具有幂律尾的映射的动力学
Dynamics of a map with power-law tail
摘要：
本文分析了一个最初在种群生态学研究中提出的一维分段连续离散模型。该映射由一个线性部分和一个幂律递减部分组成，有三个参数。该系统既有规则行为又有混沌行为。我们研究数值，部分，解析不同的分岔结构。特别有趣的是描述的突然过渡秩序到混沌介导的吸引子由无限数量的极限环，只有有限数量的不同时期。结果表明，幂律块在地图是在这种类型的分歧的起源。系统表现出内部危机和危机诱发的不稳定性。
英文摘要：
We analyze a one-dimensional piecewise continuous discrete model proposed originally in studies on population ecology. The map is composed of a linear part and a power-law decreasing piece, and has three parameters. The system presents both regular and chaotic behavior. We study numerically and, in part, analytically different bifurcation structures. Particularly interesting is the description of the abrupt transition order-to-chaos mediated by an attractor made of an infinite number of limit cycles with only a finite number of different periods. It is shown that the power-law piece in the map is at the origin of this type of bifurcation. The system exhibits interior crises and crisis-induced intermittency.
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