Dong Yujiao, Guo Rongrong, Liang Yan, Yang Jinqiao, Wang Guangyi
Institute of Modern Circuit and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018, China.
College of Computer and Information Engineering, Qilu Institute of Technology, Jian 250200, China.
Chaos. 2024 Aug 1;34(8). doi: 10.1063/5.0219075.
Brain-like dynamics require third-order or higher-order complexity. In order to investigate the coupling neuromorphic behaviors of identical third-order memristive neurons, this paper begins with the aim of exploring two identical neuron based dynamics under distinct operating regimes and coupling strengths. Without coupling, the single neuron can exhibit resting states, periodic spikes, or chaos depending on the bias condition. The uncoupled resting neurons can be activated by resistive coupling, inducing inhomogeneous resting states (static Smale paradox) and inhomogeneous spikes (dynamic Smale paradox) due to the edge of chaos regime. Considering the single neuron at the periodic spikes or chaotic states, the coupled neurons can mimic shocking oscillation death, non-periodic asynchronization, and periodic synchronization via the Hopf bifurcation theory. From the above analyses, an artificial ring neural network is constructed using 100 memristive neurons and resistive synapses to further study the coupled mechanism, generating exotic spatiotemporal patterns such as chimera death, amplitude chimera, solitary states, and asynchronization because of symmetry breaking. This sheds new light on exploring exotic spatiotemporal patterns of networks based on memristive neurons from the perspective of the nonlinear circuit theory.
类脑动力学需要三阶或更高阶的复杂性。为了研究相同三阶忆阻神经元的耦合神经形态行为，本文首先旨在探索在不同工作模式和耦合强度下基于两个相同神经元的动力学。在无耦合情况下，单个神经元可根据偏置条件呈现静息状态、周期性尖峰或混沌状态。未耦合的静息神经元可通过电阻耦合被激活，由于混沌区域的边缘，会诱导出不均匀的静息状态（静态斯梅尔悖论）和不均匀的尖峰（动态斯梅尔悖论）。考虑处于周期性尖峰或混沌状态的单个神经元，耦合神经元可通过霍普夫分岔理论模拟振荡死亡、非周期性异步和周期性同步。通过上述分析，利用100个忆阻神经元和电阻突触构建了一个人工环形神经网络，以进一步研究耦合机制，由于对称性破缺产生了奇异的时空模式，如嵌合体死亡、振幅嵌合体、孤立状态和异步。这从非线性电路理论的角度为探索基于忆阻神经元的网络奇异时空模式提供了新的思路。
