Institute of Nanoscience and Nanotechnology, National Center for Scientific Research "Demokritos", Athens, Greece.
Department of Mathematical Sciences, University of Essex, Wivenhoe Park, UK.
Adv Exp Med Biol. 2021;1338:247-258. doi: 10.1007/978-3-030-78775-2_30.
We study the influence of broken connectivity and frequency disorder in systems of coupled neuronal oscillators. Under nonlocal coupling, systems of nonlinear oscillators, such as Kuramoto, FitzHugh-Nagumo, or integrate-and-fire oscillators, demonstrate nontrivial synchronization patterns. One of these patterns is the "chimera state," which consists of coexisting coherent and incoherent domains. In networks of biological neurons, the connectivity is not always perfect, but might be locally broken or interrupted due to pathologies, neuron degenerative disorders, or accidents. Our simulations show that destructed connectivity drastically affects synchronization, driving the coherent parts of the chimera state to cover symmetrically the region where the anomaly is located. The network synchronization decreases with the size of the destructed region as evidenced by the Kuramoto synchronization index. To the contrary, when keeping the connectivity of all nodes intact, altering the frequency in a block of oscillators drives the incoherent part of the chimera state toward the anomaly. This work is in line with recent dynamical approaches aiming to locate anomalies in the structure of brain networks, in particular when the anomalies have small, difficult-to-detect sizes.
我们研究了在耦合神经元振荡器系统中，连接中断和频率紊乱的影响。在非局部耦合下，诸如 Kuramoto、FitzHugh-Nagumo 或积分-点火振荡器等非线性振荡器系统表现出非平凡的同步模式。其中一种模式是“嵌合体状态”，它由共存的相干和非相干域组成。在生物神经元网络中，连接并不总是完美的，但由于病变、神经元退行性疾病或事故等原因，连接可能会局部中断或中断。我们的模拟表明，破坏的连接会严重影响同步，使嵌合体状态的相干部分对称地覆盖异常所在的区域。网络同步随着破坏区域的大小而降低，这可以通过 Kuramoto 同步指数来证明。相反，当保持所有节点的连接完好无损时，改变振荡器块中的频率会导致嵌合体状态的非相干部分向异常移动。这项工作符合最近旨在定位脑网络结构异常的动力学方法，特别是当异常具有较小、难以检测的尺寸时。
