Spiking Neuron and Network Dynamics
Stub. Moving from the rate-based neural network models of the rest of the course to spiking neurons: single-neuron spiking dynamics, how spiking units combine into network-level dynamics, and hybrid/event-based systems — dynamical systems whose state evolves continuously between discrete, instantaneous spike events.
Corresponds to the first half of the “Spiking networks and research frontiers” unit of the syllabus (weeks 11–13) — no lecture dates posted yet for this unit; update once lectures are posted. Every earlier note in this course treated a neuron’s activity as a continuous rate variable; here the state is a continuously-evolving membrane potential punctuated by discrete, essentially instantaneous spikes, which resets the state and communicates with other neurons. This makes a spiking neuron a hybrid system: ordinary continuous-time flow dynamics (phase-space-geometry-fixed-points-and-linearization) interrupted by discrete, state-resetting events — and an event-based simulation exploits this by only updating the state when something changes, rather than on a fixed timestep grid. A spiking network’s dynamics are these hybrid single-neuron systems coupled together, so the same fixed-point and stability questions from earlier in the course now have to be asked about a system with event-driven jumps, not a smooth flow.
Outline (TODO — flesh out each)
- Single-neuron spiking dynamics
- Network dynamics of coupled spiking neurons
- Hybrid systems — continuous flow interrupted by discrete events
- Event-based simulation