论文标题

后后神经元的异质网络的复杂动力学

Complex dynamics of a heterogeneous network of Hindmarsh-Rose neurons

论文作者

Njitacke, Zeric Tabekoueng, Muni, Sishu Shankar, Seth, Soumyajit, Awrejcewicz, Jan, Kengne, Jacques

论文摘要

在这项贡献中,我们考虑了两者的集体行为以及异质耦合后玛什玫瑰(HR)神经元的网络。异质模型是由回忆2D(HR)和传统3D HR神经元制成的。通过电突触研究两个耦合神经元的模型揭示了耗散特性。当控制参数变化时,耦合的神经元模型表现出丰富的动力学,例如涉及爆发或尖峰振荡的周期性,准周期性和混乱动力学。对于弱的电耦合强度,观察到非同步运动。但是,在较高的耦合强度的情况下,观察到同步群集状态。此外,正在研究三种不同的异质拓扑结构下的环网络,最多100个,并探索了各种时空模式。发现时空模式取决于所考虑的异质网络的拓扑。通过复发图定性地揭示了一个新的聚类嵌合体状态。聚类状态在异质网络的环和星形配置中指示。单孔和双孔嵌合体已在环和环形恒星结构中揭示。最后,在PSIM仿真环境中设计和研究了两个耦合异质的等效电子电路。从设计的模拟电路获得的结果与两个耦合神经元的数学模型之间观察到了完美的匹配,这支持了我们获得的结果与伪影无关的事实。

In this contribution, we have considered the collective behavior of the two as well as the network of heterogeneous coupled Hindmarsh Rose (HR) neurons. The heterogeneous models were made of a memristive 2D (HR) and the traditional 3D HR neurons. Investigating a model of two coupled neurons through an electrical synapse reveals dissipative properties. When control parameters are varied, the coupled neuron model exhibits rich dynamics, such as the periodic, quasi-periodic, and chaotic dynamics involving either bursting or spiking oscillations. For weak electrical coupling strength, non-synchronized motion is observed. But in the case of higher coupling strength, synchronized cluster states are observed. Besides, ring-star networks of up to 100 under three different heterogeneous topologies are being investigated, and various spatiotemporal patterns are explored. It is found that the spatiotemporal patterns depend on the topology of the heterogeneous network considered. A new clustered chimera state is revealed qualitatively via the recurrence plot. The cluster states are indicated in the ring and star configurations of the heterogeneous network. Single and double-well chimera states have been revealed in the ring and ring-star structures. Finally, an equivalent electronic circuit for the two coupled heterogeneous is designed and investigated in the PSIM simulation environment. A perfect match is observed between the results obtained from the designed analog circuit and the mathematical model of the two coupled neurons, which supports the fact that our obtained results are not related to an artifact.

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