Algebraic approach to chaos induced by snapback repeller
Algebraic approach to chaos induced by snapback repeller
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DOI：
10.1145/3377006.3377016
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发表时间：
2019-12
影响因子：
0.1
通讯作者：
Bo Huang;W. Niu
中科院分区：
文献类型：
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作者：
Bo Huang;W. Niu
在这张海报中，我们展示了b[1]的结果。研究离散动力系统中混沌行为的检测问题。我们提出了一个确定给定多项式的所有零点是否在复平面上的单位圆外的代数判据。根据马罗托定理，利用该准则推导出多维离散系统发生混沌的临界代数条件。利用这些代数条件，我们将弹回驱虫引起的混沌分析问题简化为一个代数问题，并引入了一种用符号计算的方法来解决这一问题的算法。算例表明，该方法是有效的，可用于确定所有固定点都是防逆器的可能性。
In this poster we present the results of [1]. We consider the problem of detecting chaotic behaviors in discrete dynamical systems. We propose an algebraic criterion for determining whether all the zeros of a given polynomial are outside the unit circle in the complex plane. This criterion is used to deduce critical algebraic conditions for the occurrence of chaos in multi-dimensional discrete systems based on Marotto's theorem. Using these algebraic conditions we reduce the problem of analyzing chaos induced by snapback repeller to an algebraic problem, and introduce an algorithmic approach to solve this problem by means of symbolic computation. The proposed approach is effective as shown by several examples and can be used to determine the possibility that all the fixed points are snapback repellers.