标题： 非互惠霍普菲尔德网络中的临界动力学和循环记忆检索 显示英文标题

标题： Critical Dynamics and Cyclic Memory Retrieval in Non-reciprocal Hopfield Networks

摘要： 我们研究具有非互惠耦合的霍普菲尔德网络，这种耦合会引发记忆模式之间的切换。 在无记忆检索相、多个点吸引子的检索相和极限环吸引子相之间会发生动力学相变。 极限环相由两个临界区域限定：一个霍普夫分支线和一个折叠分支线，每个都有独特的动力学临界指数和对扰动的敏感性。 主方程方法数值验证了分析预测的临界行为。 我们讨论这些网络如何在循环不稳定性临界阈值附近模拟生物过程，该过程通过多步骤转换演化。 显示英文摘要

摘要： We study Hopfield networks with non-reciprocal coupling inducing switches between memory patterns. Dynamical phase transitions occur between phases of no memory retrieval, retrieval of multiple point-attractors, and limit-cycle attractors. The limit cycle phase is bounded by two critical regions: a Hopf bifurcation line and a fold bifurcation line, each with unique dynamical critical exponents and sensitivity to perturbations. A Master Equation approach numerically verifies the critical behavior predicted analytically. We discuss how these networks could model biological processes near a critical threshold of cyclic instability evolving through multi-step transitions.