It is known that saddle-node (s-n) bifurcations leave a saddle remnant (or ghost) in the region of the phase space where the annihilation of the fixed points occurred. The corresponding time delay, t d , found right after the bifurcation is known to follow the scaling law ##IMG## [http://ej.iop.org/images/1367-2630/22/9/093064/njpabb549ieqn1.gif] {${t}_{\mathrm{d}}\sim {\left({\epsilon}-{{\epsilon}}_{\mathrm{c}}\right)}^{-1/2}$} , where ϵ and ϵ c are the control parameter and its critical value, respectively. While the properties of such delays are well understood for deterministic systems, much less is known about how intrinsic noise influences this phenomenon. As a first step towards analysing this issue, in this article we explore a model with autocatalysis and a two-species hypercycle to analyse the impact of noise on delayed transitions in one- and two-dimensional dynamical systems suffering a s-n bifurcation. T...

中文翻译：

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噪声引起的鞍节点重影的稳定

众所周知，鞍形结（sn）分叉会在发生固定点an没的相空间区域中留下鞍形残余（或重影）。分叉后立即发现的相应时间延迟td遵循缩放定律## IMG ## [http://ej.iop.org/images/1367-2630/22/9/093064/njpabb549ieqn1.gif ] {$ {t} _ {\ mathrm {d}} \ sim {\ left（{\ epsilon}-{{\ epsilon}} _ {\ mathrm {c}} \ right）} ^ {-1/2} $}，其中ϵ和ϵ c分别是控制参数及其临界值。虽然对于确定性系统很好地了解了此类延迟的属性，但对于固有噪声如何影响此现象的了解还很少。作为分析此问题的第一步，在本文中，我们探索了一个具有自动催化和两个物种超循环的模型，以分析噪声对遭受分叉的一维和二维动力学系统中延迟跃迁的影响。T ...