非自治混沌系统的弱跟踪
Weak tracking in nonautonomous chaotic systems
摘要：
以往的研究表明，率诱导的转变可以发生在拉回吸引子的系统受到“参数移位”之间的两个渐近稳定的系统参数的值。对于吸引子限制在平衡或周期轨道在过去和未来的限制这样的非自治系统的情况下，这些可能会发生的参数变化通过一个临界速率。这种速率诱导的吸引子，限制到混沌吸引子在过去或未来的限制已较少研究。在本文中，我们发现了一个新的现象是与更复杂的吸引子在未来的极限：弱跟踪，其中一个拉回吸引子的系统限制到一个真子集的未来极限系统的吸引子。我们证明了弱跟踪在一个非自治的Rössler系统，并认为有无穷多个临界速率在每个拉回吸引系统的解决方案跟踪嵌入不稳定的周期轨道的未来混沌吸引子。本文还给出了弱跟踪所需的一些必要条件。
英文摘要：
Previous studies have shown that rate-induced transitions can occur in pullback attractors of systems subject to "parameter shifts" between two asymptotically steady values of a system parameter. For cases where the attractors limit to equilibrium or periodic orbit in past and future limits of such an nonautonomous systems, these can occur as the parameter change passes through a critical rate. Such rate-induced transitions for attractors that limit to chaotic attractors in past or future limits has been less examined. In this paper, we identify a new phenomenon is associated with more complex attractors in the future limit: weak tracking, where a pullback attractor of the system limits to a proper subset of an attractor of the future limit system. We demonstrate weak tracking in a nonautonomous Rössler system, and argue there are infinitely many critical rates at each of which the pullback attracting solution of the system tracks an embedded unstable periodic orbit of the future chaotic attractor. We also state some necessary conditions that are needed for weak tracking.
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