We consider a system of two coupled identical logistic maps, which in isolation demonstrate stable equilibrium modes. Under increasing coupling strength, this system exhibits transitions from initial equilibrium regime to synchronized oscillatory behavior with complex modes, both regular (periodic or quasiperiodic) and chaotic. Moreover, the coupled subsystem can demonstrate synchronization with anti-phase oscillations in tonic or burst form. A novelty of this paper is related to analysis of noise-induced deformations of these corporative oscillatory regimes. For this model, the following constructive stochastic effects are studied: (i) noise-induced temporal destruction of the anti-phase synchronization with transition from tonic to burst oscillations, (ii) noise-induced destruction of 2-torus with the transition from quasiperiodic oscillations to the bursting, (iii) stochastic transformations of burst oscillations from regular to chaotic. An important role of transients and “riddled” basins in the study of stochastic shifts of crisis bifurcation points is discussed. For the analytical investigation of these phenomena, a method based on the stochastic sensitivity of attractors (discrete cycles and tori) and confidence domains is applied.

我们考虑一个由两个耦合的相同逻辑图组成的系统，这些图独立地显示出稳定的平衡模式。在增加耦合强度的情况下，该系统表现出从初始平衡状态到具有复杂模式（规则（周期性或准周期性）和混沌）的同步振动行为的转变。此外，耦合的子系统可以显示与补品或猝发形式的反相振荡的同步。本文的新颖性与这些公司振荡制度的噪声引起的变形的分析有关。对于此模型，研究了以下建设性的随机效应：（i）噪声引起的反相​​同步的时间破坏，从音调到突发振荡的过渡，（ii）噪声引起的2-torus破坏，从准周期振荡过渡到爆发，（iii）突发振荡从规则到随机的随机转变。讨论了瞬态和“谜底”盆地在研究危机分叉点的随机变化中的重要作用。为了对这些现象进行分析研究，采用了一种基于吸引子的随机敏感性（离散周期和花托）和置信域的方法。