标题： 超混沌和$N$-维神经元格子中的复杂动力学状态 显示英文标题

标题： Hyperchaos and complex dynamical regimes in $N$-dimensional neuron lattices

摘要： 我们研究了$N$维非混沌鲁尔科夫神经元组成的格子通过电流耦合的动力学。我们考虑了最近邻和次近邻耦合，同质和异质神经元，以及在广泛范围的电耦合强度下的小规模和大规模格子。随着耦合强度的变化，神经元表现出多种复杂的动力学状态，包括非同步混沌放电、局部拟爆发、同步混沌爆发和同步超混沌。对于更高空间维度的格子，我们发现了由于许多连接的神经元的“破坏性干涉”而产生的动力学效应以及从协调的阈值穿越中的微型“相变”。在大规模二维和三维神经元格子中，我们观察到局部同步、准同步和滞后同步等涌现动力学。这些结果展示了多个空间维度中耦合神经元所涌现的丰富动力学，突显了维度、连通性和异质性如何关键地塑造神经系统的集体行为。 显示英文摘要

摘要： We study the dynamics of $N$-dimensional lattices of nonchaotic Rulkov neurons coupled with a flow of electrical current. We consider both nearest-neighbor and next-nearest-neighbor couplings, homogeneous and heterogeneous neurons, and small and large lattices over a wide range of electrical coupling strengths. As the coupling strength is varied, the neurons exhibit a number of complex dynamical regimes, including unsynchronized chaotic spiking, local quasi-bursting, synchronized chaotic bursting, and synchronized hyperchaos. For lattices in higher spatial dimensions, we discover dynamical effects arising from the ``destructive interference'' of many connected neurons and miniature ``phase transitions'' from coordinated spiking threshold crossings. In large two- and three-dimensional neuron lattices, we observe emergent dynamics such as local synchronization, quasi-synchronization, and lag synchronization. These results illustrate the rich dynamics that emerge from coupled neurons in multiple spatial dimensions, highlighting how dimensionality, connectivity, and heterogeneity critically shape the collective behavior of neuronal systems.