Bashkirtseva Irina, Ryashko Lev
Department of Theoretical and Mathematical Physics, Ural Federal University, Lenina, 51, 620000 Ekaterinburg, Russia.
Chaos. 2021 May;31(5):053101. doi: 10.1063/5.0050613.
A system of two coupled map-based oscillators is studied. As units, we use identical logistic maps in two-periodic modes. In this system, increasing coupling strength significantly changes deterministic regimes of collective dynamics with coexisting periodic, quasiperiodic, and chaotic attractors. We study how random noise deforms these dynamical regimes in parameter zones of mono- and bistability, causes "order-chaos" transformations, and destroys regimes of in-phase and anti-phase synchronization. In the analytical study of these noise-induced phenomena, a stochastic sensitivity technique and a method of confidence domains for periodic and multi-band chaotic attractors are used. In this analysis, a key role of chaotic transients and geometry of "riddled" basins is revealed.
研究了一个由两个基于映射的耦合振荡器组成的系统。作为单元，我们使用处于双周期模式的相同逻辑斯谛映射。在这个系统中，增加耦合强度会显著改变集体动力学的确定性状态，其中共存着周期、准周期和混沌吸引子。我们研究随机噪声如何在单稳态和双稳态的参数区域中使这些动力学状态变形，导致“有序 - 混沌”转变，并破坏同相和反相同步状态。在对这些噪声诱导现象的分析研究中，使用了随机灵敏度技术以及针对周期和多频带混沌吸引子的置信域方法。在该分析中，揭示了混沌瞬态和“布满孔洞”的吸引盆几何形状的关键作用。
