论文标题
非自主混沌系统中的弱跟踪
Weak tracking in nonautonomous chaotic systems
论文作者
论文摘要
先前的研究表明，在系统参数的两个渐近稳定值之间，速率诱导的转变可能发生在系统的回调吸引子中。对于吸引子在这种非自主系统的过去和将来限制中限制了平衡或周期轨道的情况下，当参数变化通过临界率时，它们可能会发生。对过去或将来的限制中限制混乱吸引子的吸引子的这种速率引起的过渡已经受到较少的检查。在本文中，我们确定了一种新现象与未来限制中更复杂的吸引子相关联：弱跟踪，在该系统中，系统的回调吸引子限制了未来极限系统吸引人的适当子集。我们在非自主rössler系统中表现出较弱的跟踪，并认为每个关键的速率在每种过程中都有无限的关键速率吸引系统的解决方案跟踪未来混乱吸引子的嵌入式不稳定的周期性轨道。我们还规定了一些弱跟踪所需的必要条件。
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.
