Localization of hidden attractors is one of the most challenging tasks in the nonlinear dynamics due to deficiency of properly justified analytical and numerical procedures. But understanding about the emergence of such unexpected occurrence of hidden attractors is desirable, because that can help to diminish the unexpected switch from one attractor to another undesired behavior. We propose a novel autonomous three-dimensional system exhibiting hidden attractor. These attractors can not be tracked using perpetual points. The reason behind this inefficiency is explained using theory of differential equations. Our system consists a slow manifold depicted through the time-series, although the system has no equilibrium points or such multiplicative parameters. We also discuss the behavior of the attractor using time-series analysis, bifurcation theory, Lyapunov spectrum and Kaplan-Yorke dimension. Moreover, the attractor no longer exists for a range of parameter values due to sudden change of strange attractors indicating a possible inverse crisis route to chaos.

中文翻译：

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隐藏的吸引子：没有平衡的新混沌系统

由于缺乏合理的分析和数值程序，隐藏吸引子的定位是非线性动力学中最具挑战性的任务之一。但是了解这种隐藏吸引子的意外发生的出现是可取的，因为这可以帮助减少从一个吸引子到另一种不良行为的意外切换。我们提出了一种新颖的具有隐藏吸引子的自主三维系统。不能使用永久点来跟踪这些吸引子。使用微分方程理论解释了这种低效率背后的原因。我们的系统包括一个通过时间序列描述的慢流形，尽管该系统没有平衡点或此类乘法参数。我们还使用时间序列分析，分叉理论来讨论吸引子的行为，Lyapunov谱和Kaplan-Yorke维。此外，由于奇怪的吸引子的突然变化，表明存在可能的逆向危机之路，因此吸引子不再存在一定范围的参数值。