We analyze mechanisms of stochastic transformations of complex oscillatory regimes in the 2D Rulkov model with the smooth map. In the birhythmicity parametric zone with coexistence of periodic and chaotic oscillations, noise-induced transitions from regular spiking to chaotic bursting are studied. In the monorhythmicity zone of regular periodic oscillations, the stochastic phenomenon of the systematic shift of probability distributions with generation of a phantom chaotic attractor is discovered and analyzed. The relationship of this phenomenon with the presence of transient chaotic attractors in the original deterministic model is revealed and discussed. For parametric analysis of these phenomena, we apply the confidence ellipses method based on the stochastic sensitivity technique.

中文翻译：

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双节律神经元模型中噪声诱导的混沌和幻影吸引子的产生


我们使用平滑图分析了 2D Rulkov 模型中复杂振荡状态的随机变换机制。在周期性和混沌振荡共存的双节律性参数区中，研究了噪声诱导从规则尖峰到混沌爆发的转变。在有规律的周期性振荡的单节律性区，发现并分析了概率分布系统性移动随幻影混沌吸引子的产生而发生的随机现象。揭示和讨论了这种现象与原始确定性模型中瞬态混沌吸引子存在的关系。为了对这些现象进行参数分析，我们应用了基于随机灵敏度技术的置信椭圆方法。