2.兰州交通大学数理学院
摘要：为了探究噪声对神经元的放电模式和神经元之间的同步稳定性的影响，考虑Morris-Lecar(ML)神经元模型，通过单参数及双参数分岔图、李亚普洛夫指数图、相图详细探究了其动力学行为，结果表明系统具有丰富的分岔行为，对初值敏感，并表现出多稳态共存现象。其次，通过磁控忆阻器耦合ML神经元，对比了加入噪声前后耦合系统的能量平衡和同步模式。研究发现，无论是否加入噪声，耦合系统都可以达到能量平衡，实现完全同步。这些结果为识别突触自适应性提供新的指引。关键词：高斯白噪声；完全同步；近似同步；Morris-Lecar神经元模型；Hamilton能量
基金资助:2024年重庆对外经贸学院科研项目(KYZK2024031)； 甘肃省自然科学基金重点项目(23JRRA861)Bifurcation Analysis and Energy Modulation of ML Neurons Under Noise
JIANG Lingfeng1, AN Xinlei2, LI Hongwei1, HE Weijun1
1.School of Mathematics and Computer Science, Chongqing College of International Business and Economics2.School of Mathematics and Physics, Lanzhou Jiaotong UniversityAbstract: 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.Keywords: Gaussian white noise; complete synchronization; quasi-synchronization; morris-Lecar neuron model; hamilton energy![]()
蒋玲凤（1999-）女，四川资阳人，硕士研究生，主要研究方向为非线性动力学。
安新磊（1983-），男，河南开封人，博士后，教授，主要研究方向为非线性动力学。李宏伟（1997-），男，安徽合肥人，硕士研究生，主要研究方向为偏微分方程。何伟军（1998-），男，重庆丰都人，硕士研究生，主要研究方向为偏微分方程。蒋玲凤,安新磊,李宏伟,等.噪声作用下ML神经元的分岔分析和能量调制[DB/OL].(2025-01-08).http://kns.cnki.net/kcms/detail/37.1402.N.20250108.1115.004.html.
