ABSTRACT

With the consideration of electromagnetic induction generated by the difference of membrane potentials between two adjacent neurons, a five-dimensional (5-D) memristor-coupled FitzHugh–Nagumo (FHN) bi-neuron model derived from connecting two FHN neurons with the memristive electromagnetic induction is presented. Then, with the 5-D memristor-coupled FHN bi-neuron model, the equilibrium states and their stabilities are explored by theoretical and numerical analyses. It is indicated that the proposed model has two non-zero equilibrium states with the same stability of unstable saddle-focus or unstable saddle point associating to the considered model parameters. The parameter-associated electrical activities of periodic, quasi-periodic, and chaotic behaviors are disclosed by bifurcation plots, dynamical maps, phase plane plots and further confirmed by 0–1 tests. Besides, the phenomena of initial-associated bi-stability with the coexistence of chaotic and periodic behaviors, as well as the riddled attraction basin, are revealed by local attraction basins and phase plane plots. Furthermore, based on field programmable gate array (FPGA), a digitally implemented electronic circuit is made, from which the electrical activities are experimentally captured to verify the numerical ones.

摘要

考虑到两个相邻神经元之间的膜电位差异产生的电磁感应，将两个 FHN 神经元与忆阻电磁学连接起来，得到了一个五维 (5-D) 忆阻器耦合 FitzHugh-Nagumo (FHN) 双神经元模型。归纳提出。然后，使用 5-D 忆阻器耦合 FHN 双神经元模型，通过理论和数值分析探索平衡状态及其稳定性。结果表明，所提出的模型具有两个非零平衡状态，与所考虑的模型参数相关的不稳定鞍点或不稳定鞍点具有相同的稳定性。周期性、准周期性和混沌行为的参数相关电活动通过分岔图、动力学图、相平面图并通过 0-1 测试进一步确认。此外，局部吸引盆地和相平面图揭示了初始相关双稳态与混沌和周期性行为并存的现象，以及千疮百孔的吸引盆地。此外，基于现场可编程门阵列（FPGA），制作了数字实现的电子电路，从中通过实验捕获电活动以验证数字活动。