在非互惠的霍普菲尔德网络中,关键动力学和循环记忆检索
Shuyue Xue1,2, Mohammad Maghrebi1, George I Mias1,3,4
1Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA.
ArXiv
|January 13, 2025
概括
这项研究探讨了非互惠合的霍普菲尔德网络,揭示了临界值附近的内存检索,点吸引器和极限周期吸引器之间的动态相位过渡.
科学领域:
- 计算神经科学是一种计算神经科学.
- 复杂系统的动态 复杂系统的动态
- 统计物理学的统计物理.
背景情况:
- 霍普菲尔德网络是关联记忆的基础模型.
- 非互惠合引入了传统模型中不存在的新动态.
- 了解相位过渡对于复杂的系统行为至关重要.
研究的目的:
- 调查非互惠合对霍普菲尔德网络动态的影响.
- 识别和描述记忆检索的不同阶段.
- 分析在极限周期阶段边界的关键行为.
主要方法:
- 网络动态的分析推导.
- 使用主方程方法进行数值验证.
- 对临界指数和对扰动的敏感性的分析.
主要成果:
- 确定了三个不同的动态阶段:没有内存,点吸引器内存和极限周期内存.
- 通过Hopf和折叠分叉线来表征极限周期相位边界.
- 通过数值模拟验证了关键行为的分析预测.
结论:
- 霍普菲尔德网络中的非互惠合导致了丰富的动态过渡.
- 鉴定到的关键区域为接近周期性不稳定的系统提供了洞察力.
- 这些发现在模拟表现出多步过渡的生物过程中具有潜在的应用.
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