Bifurcation Analysis and Energy Modulation of ML Neurons Under Noise
JIANG Lingfeng1, AN Xinlei2, LI Hongwei1, HE Weijun1, LENG Zhenbei1
1. School of Mathematics and Computer Science, Chongqing College of International Business and Economics, Chongqing 401520, China; 2. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China
Abstract：To investigate the effect of noise on the discharge patterns of neurons and the synchronization stability between neurons, this paper considers the Morris-Lecar (ML) neuron model and explores its dynamical behavior by means of single-two-parameter bifurcation diagrams, Lyapunov exponent diagrams, and phase diagrams. The results show that the system not only exists rich bifurcation behaviors but also is sensitive to the initial value and exhibits multi-stable coexistence states. Next, the energy balance and synchronization patterns of the coupled system before and after the addition of noise are compared by coupling the ML neurons through a magnetic flux-controlled memristor. It is found that the coupled system can achieve energy balance and complete synchronization regardless of whether noise is added. These results provide new guidelines for identifying synaptic adaptability.
蒋玲凤, 安新磊, 李宏伟, 何伟军, 冷震北. 噪声作用下ML神经元的分岔分析和能量调制[J]. 复杂系统与复杂性科学, 2026, 23(3): 104-111.
JIANG Lingfeng, AN Xinlei, LI Hongwei, HE Weijun, LENG Zhenbei. Bifurcation Analysis and Energy Modulation of ML Neurons Under Noise[J]. Complex Systems and Complexity Science, 2026, 23(3): 104-111.
[1] 马军. 功能神经元建模及动力学若干问题[J]. 广西师范大学学报(自然科学版), 2022, 40(5): 307-323. MA J. Dynamics and model approach for functional neurons[J]. Journal of Guangxi Normal University (Natural Science Edition), 2022, 40(5): 307-323. [2] YU X H, Bao H, Chen M, et al. Energy balance via memristor synapse in Morris-Lecar two-neuron network with FPGA implementation[J]. Chaos, Solitons & Fractals, 2023, 171: 113442. [3] FITZHUGH R. Mathematical models of threshold phenomena in the nerve membrane[J]. The Bulletin of Mathematical Biophysics, 1955, 17(4): 257-278. [4] 李馨雅, 闵富红, 相惟康, 等. 新型FitzHugh-Nagumo神经元电路动力学分析[J]. 南京师范大学学报(工程技术版), 2023, 23(4): 1-9. LI X Y, MIN F H, XIANG W K, et al. Dynamical analysis of a novel FitzHugh-Nagumo neuron circuit[J]. Journal of Nanjing Normal University (Engineering), 2023, 23(4): 1-9. [5] IZHIKEVICH E M. Neural excitability, spiking and bursting[J]. International Journal of Bifurcation and Chaos, 2000, 10(6): 1171-1266. [6] ZHANG L, AN X L, XIONG L, et al. Synchronization, extreme multistability, and its control for a field coupled neurons with time delays[J]. International Journal of Modern Physics B, 2022, 36(19): 2250114. [7] HOU B, MA J, YANG F F. Energy-guided synapse coupling between neurons under noise[J]. Journal of Biological Physics, 2023, 49(1): 49-76. [8] 邬开俊. Hindmarsh-Rose神经元模型的双参数分岔特性及耦合同步研究[D]. 兰州: 兰州交通大学, 2017. WU K J. The double parameter bifurcation characteristic and coupling synchronization of Hindmarsh-Rose neural model[D]. Lanzhou: Lanzhou Jiaotong University, 2017. [9] ZHOU P, ZHANG X F, MA J. How to wake up the electric synapse coupling between neurons?[J]. Nonlinear Dynamics, 2022, 108(2): 1681-1695. [10] 安新磊, 张莉. 一类忆阻神经元的电活动多模振荡及Hamilton能量反馈控制[J]. 力学学报, 2020, 52(4): 1174-1188. AN X L, ZHANG L. Multi-mode oscillations and Hamilton energy feedback control of a class of memristor neuron[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 1174-1188. [11] 黄微, 韦笃取. 忆阻Morris-Lecar神经网络的同步行为研究[J]. 广西师范大学学报(自然科学版), 2024, 42(1): 67-78. HUANG W, WEI D Q. Synchronization behavior of memristor Morris-Lecar neural networks[J]. Journal of Guangxi Normal University (Natural Science Edition), 2024, 42(1): 67-78. [12] 王宾, 李海啸, 陈蓉蓉. 一种改进类提升方案的双彩色图像加密系统[J]. 计算机科学, 2024, 51(S1): 968-978. WANG B, LI H X, CHEN R R. Dual-color image encryption system with improved lifting-like scheme[J]. Computer science, 2024, 51(S1): 968-978. [13] WANG C Y, ZHANG J Q, WU Z X, et al. Collective firing patterns of neuronal networks with short-term synaptic plasticity[J]. Physical Review E, 2021, 103(2): 022312. [14] 房涛, 范影乐, 蔡哲飞, 等. FHN神经元小世界网络随机共振下的弱信号增强[J]. 传感技术学报, 2021, 34(3): 361-369. FANG T, FAN Y Y, CAI Z F, et al. Weak signal enhancement under stochastic resonance of FHN neuron small-world network[J]. Chinese Journal of Sensors and Actuators, 2021, 34(3): 361-369. [15] VELI B, ALI C. Stochastic resonance in a single autapse-coupled neuron[J]. Chaos, Solitons & Fractals, 2023, 175(2): 114059. [16] SEMENOV V, BUKH A, SEMENOVA N. Delay-induced self-oscillation excitation in the Fitzhugh-Nagumo model: regular and chaotic dynamics[J]. Chaos, Solitons & Fractals, 2023, 172: 113524. [17] ZHOU P, XU Y, MA J. Dynamical and coherence resonance in a photoelectric neuron under autaptic regulation[J]. Physica A: Statistical Mechanics and Its Applications, 2023, 620: 128746. [18] AN X L, QIAO S. The hidden, period-adding, mixed-mode oscillations and control in a HR neuron under electromagnetic induction[J]. Chaos, Solitons & Fractals, 2021, 143: 110587.
