Provata Astero, Almirantis Yannis, Li Wentian
Institute of Nanoscience and Nanotechnology, National Center for Scientific Research "Demokritos", 15341 Athens, Greece.
Institute of Biosciences and Applications, National Center for Scientific Research "Demokritos", 15341 Athens, Greece.
Entropy (Basel). 2025 Feb 28;27(3):257. doi: 10.3390/e27030257.
Chimera states and bump states are collective synchronization phenomena observed independently (in different parameter regions) in networks of coupled nonlinear oscillators. And while chimera states are characterized by coexistence of coherent and incoherent domains, bump states consist of alternating active and inactive domains. The idea of multistable plasticity in the network connections originates from brain dynamics where the strength of the synapses (axons) connecting the network nodes (neurons) may change dynamically in time; when reaching the steady state the network connections may be found in one of many possible values depending on various factors, such as local connectivity, influence of neighboring cells etc. The sign of the link weights is also a significant factor in the network dynamics: positive weights are characterized as excitatory connections and negative ones as inhibitory. In the present study we consider the simplest case of bistable plasticity, where the link dynamics has only two fixed points. During the system/network integration, the link weights change and as a consequence the network organizes in excitatory or inhibitory domains characterized by different synaptic strengths. We specifically explore the influence of bistable plasticity on collective synchronization states and we numerically demonstrate that the dynamics of the linking may, under special conditions, give rise to co-existence of bump-like and chimera-like states simultaneously in the network. In the case of bump and chimera co-existence, confinement effects appear: the different domains stay localized and do not travel around the network. Memory effects are also reported in the sense that the final spatial arrangement of the coupling strengths reflects some of the local properties of the initial link distribution. For the quantification of the system's spatial and temporal features, the global and local entropy functions are employed as measures of the network organization, while the average firing rates account for the network evolution and dynamics. In particular, the spatial minima of the local entropy designate the transition points between domains of different synaptic weights in the hybrid states, while the number of minima corresponds to the number of different domains. In addition, the entropy deviations signify the presence of chimera-like or bump-like states in the network.
嵌合态和脉冲态是在耦合非线性振荡器网络中独立观察到的（在不同参数区域）集体同步现象。虽然嵌合态的特征是相干域和非相干域共存，但脉冲态由交替的活跃域和非活跃域组成。网络连接中多稳态可塑性的概念源于脑动力学，其中连接网络节点（神经元）的突触（轴突）强度可能随时间动态变化；当达到稳态时，网络连接可能会根据各种因素（如局部连通性、相邻细胞的影响等）处于许多可能值之一。连接权重的符号也是网络动力学中的一个重要因素：正权重表征为兴奋性连接，负权重表征为抑制性连接。在本研究中，我们考虑双稳态可塑性的最简单情况，其中连接动力学只有两个固定点。在系统/网络整合过程中，连接权重发生变化，结果网络组织成具有不同突触强度的兴奋性或抑制性域。我们具体探讨了双稳态可塑性对集体同步态的影响，并通过数值证明，在特殊条件下，连接动力学可能导致网络中同时共存脉冲状和嵌合状状态。在脉冲和嵌合共存的情况下，会出现限制效应：不同的域保持局部化，不会在网络中移动。还报道了记忆效应，即耦合强度的最终空间排列反映了初始连接分布的一些局部特性。为了量化系统的空间和时间特征，全局和局部熵函数被用作网络组织的度量，而平均发放率则说明了网络的演化和动力学。特别是，局部熵的空间最小值指定了混合态中不同突触权重域之间的过渡点，而最小值的数量对应于不同域的数量。此外，熵偏差表明网络中存在嵌合状或脉冲状状态。
