In neural circuits, synaptic strengths influence neuronal activity by shaping network dynamics, and neuronal activity influences synaptic strengths through activity-dependent plasticity. Motivated by this fact, we study a recurrent-network model in which neuronal units and synaptic couplings are interacting dynamic variables, with couplings subject to Hebbian modification with decay around quenched random strengths. Rather than assigning a specific role to the plasticity, we use dynamical mean-field theory and other techniques to systematically characterize the neuronal-synaptic dynamics, revealing a rich phase diagram. Adding Hebbian plasticity slows activity in chaotic networks and can induce chaos in otherwise quiescent networks. Anti-Hebbian plasticity quickens activity and produces an oscillatory component. Analysis of the Jacobian shows that Hebbian and anti-Hebbian plasticity push locally unstable modes toward the real and imaginary axes, explaining these behaviors. Both random-matrix and Lyapunov analysis show that strong Hebbian plasticity segregates network timescales into two bands with a slow, synapse-dominated band driving the dynamics, suggesting a flipped view of the network as synapses connected by neurons. For increasing strength, Hebbian plasticity initially raises the complexity of the dynamics, measured by the maximum Lyapunov exponent and attractor dimension, but then decreases these metrics, likely due to the proliferation of stable fixed points. We compute the marginally stable spectra of such fixed points as well as their number, showing exponential growth with network size. In chaotic states with strong Hebbian plasticity, a stable fixed point of neuronal dynamics is destabilized by synaptic dynamics, allowing any neuronal state to be stored as a stable fixed point by halting the plasticity. This phase of freezable chaos offers a new mechanism for working memory.

翻译：在神经回路中，突触强度通过塑造网络动力学影响神经元活动，而神经元活动则通过活动依赖可塑性影响突触强度。受此事实启发，我们研究了一个递归网络模型，其中神经元单元与突触耦合作为相互作用的动态变量，耦合遵循围绕淬火随机强度的衰减型赫布修正。我们并未为可塑性指定特定角色，而是利用动力学平均场理论及其他技术系统地表征神经元-突触动力学，揭示出丰富的相图。添加赫布可塑性会减缓混沌网络的动力学，并在原本静止的网络中诱导混沌。反赫布可塑性则加速动力学并产生振荡成分。雅可比矩阵分析表明，赫布与反赫布可塑性分别将局部不稳定模推向实轴与虚轴，从而解释了上述行为。随机矩阵分析与李雅普诺夫分析均显示，强赫布可塑性将网络时间尺度划分为两个频带，其中以突触主导的慢速频带驱动动力学，暗示了一种将网络视为由神经元连接的突触的翻转视角。随着赫布可塑性强度增加，动力学复杂度（以最大李雅普诺夫指数与吸引子维度衡量）先升后降，这可能是由于稳定不动点大量涌现。我们计算了这些不动点的边缘稳定谱及其数量，发现其随网络规模呈指数增长。在强赫布可塑性导致的混沌态中，突触动力学使神经元动力学的稳定不动点失稳，通过终止可塑性可存储任意神经元状态为稳定不动点。这种可冻结混沌相为工作记忆提供了新机制。