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 already 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, respectively, 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. Finally, 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.

中文翻译：

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耦合神经元突触动力学理论

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，而神经元活动通过活动依赖性可塑性影响突触强度。受此事实的启发，我们研究了一种循环网络模型，其中神经元单元和突触耦合是相互作用的动态变量，耦合受到赫布修正的影响，并在淬灭的随机强度周围衰减。我们没有为可塑性分配特定的角色，而是使用动态平均场理论和其他技术来系统地表征神经元突触动力学，揭示丰富的相图。添加赫布可塑性会减慢已经混乱的网络的活动速度，并可能在原本静止的网络中引发混乱。反赫布塑性加速了活动并产生振荡成分。雅可比矩阵的分析表明，赫布塑性和反赫布塑性分别将局部不稳定模式推向实轴和虚轴，从而解释了这些行为。随机矩阵和李亚普诺夫分析都表明，强大的赫布可塑性将网络时间尺度分为两个带，其中一个缓慢的、由突触主导的带驱动动力学，这表明网络的翻转视图是由神经元连接的突触。为了增加强度，赫布塑性最初提高了动力学的复杂性，通过最大李雅普诺夫指数和吸引子维数来衡量，但随后降低了这些指标，这可能是由于稳定不动点的扩散。我们计算了这些固定点的边际稳定谱及其数量，显示出随着网络规模的指数增长。最后，在具有强赫布可塑性的混沌状态下，神经元动力学的稳定固定点会被突触动力学破坏，从而允许通过停止可塑性将任何神经元状态存储为稳定的固定点。这一可冻结的混乱阶段为工作记忆提供了一种新的机制。