Vulnerability of Synchronization in Complex Networks due to the Existence of Chaotic Saddles

混沌鞍点存在导致复杂网络同步的脆弱性

• 批准号: 454054251
• 负责人: Professorin Dr. Ulrike Feudel
• 金额: --
• 依托单位: Institut für Chemie und Biologie des Meeres (ICBM)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/454054251?language=en
• 关键词: Vulnerability; Synchronization; Complex; Networks; due

The main objective of this proposal is to study the role of transient chaos in networked systems. The presence of chaotic saddles can lead to complete desynchronization of initially completely synchronized networks by perturbing one unit in the network at a particular time-instant (state-dependent vulnerability of synchronization). We will investigate the dynamical origin of the transition from the globally stable synchronized state to the completely desynchronized state, and clarify whether even a chaotic attractor instead of a saddle is established depending on the coupling strength of the units and the network topology. Furthermore, we will study the statistical properties of this super-persistent chaotic behavior e.g. the violation of the scaling laws for transient chaos and compare it with noise-induced attractors to find commonalities and differences. Moreover, we will identify different classes of systems in which state-dependent vulnerability occurs to prove its generality. Those classes are related with the mechanisms in which chaotic saddles appear: basin-boundary metamorphosis, boundary crisis and period-adding cascades. Finally, we will study different applications in ecology as well as in brain and heart dynamics in order to design control strategies either to keep the synchronized state stable or to break synchrony.

该方案的主要目的是研究瞬时混沌在网络系统中的作用。通过在特定时刻扰动网络中的一个单元(依赖于状态的同步脆弱性)，混沌鞍点的存在可能导致最初完全同步的网络完全去同步。我们将研究从全局稳定的同步态到完全去同步态的转变的动力学起源，并阐明是否甚至建立混沌吸引子而不是鞍座取决于单元的耦合强度和网络拓扑。此外，我们将研究这种超持久混沌行为的统计性质，例如对瞬时混沌的标度律的违反，并将其与噪声诱导的吸引子进行比较，以找到共同点和不同点。此外，我们将识别出现状态依赖漏洞的不同类别的系统，以证明其普遍性。这些类别与混沌鞍点出现的机制有关：盆地边界变形、边界危机和加周期级联。最后，我们将研究在生态学以及脑和心脏动力学中的不同应用，以设计控制策略来保持同步状态的稳定或打破同步。