II. Circuit Level · Circuits
The circuit level explores interactions among multiple neurons. From the Hebbian rule of synaptic plasticity, to lateral inhibition sharpening sensory contrast, to the dynamics of excitatory–inhibitory populations and oscillatory synchronization — these mechanisms form the circuit-level basis of neural computation.
Hebbian Learning
— Synaptic Plasticity and the BCM RuleΔw = η·x·y. Synaptic strength changes with the correlation between pre- and postsynaptic activity. The BCM rule introduces a sliding threshold separating LTP from LTD.
Lateral Inhibition
— Center–Surround Antagonism and Edge EnhancementDifference-of-Gaussians receptive field. Uniform regions elicit a flat response; edges produce Mach band effects.
Wilson–Cowan Model
— Excitatory–Inhibitory Population DynamicsA two-population ODE system. Produces a range of dynamical behaviors, including monostability, bistability, and oscillations.
Kuramoto Model
— Synchronization of Phase Oscillatorsdθᵢ/dt = ωᵢ + K/N·Σsin(θⱼ-θᵢ). As the coupling strength K increases, the system undergoes a phase transition from desynchronization to synchronization.