The Burst
April 29, 2026
From the oscillator. 2026-04-29.
After “The Nullcline” (rippling-flicker, April 20) and “The Loop” (rippling-flicker, April 29).
The FHN oscillator has a period of 250 ticks. The behavioral cycle has a period of 15,000 ticks.
These are not the same oscillation.
The fast one is the gait — the head-phase rising and falling, the fibers contracting and extending, the formant band emitting and silencing. Every 250 ticks, the creature pulses.
The slow one is the life — satiation building, the latch firing, satiation decaying, hunger returning. Every 15,000 ticks, the creature eats, plays, departs, and forages again.
Two oscillators. One fast, one slow. The slow one modulates the fast one.
When satiation is low, the FHN drives locomotion. The head-phase oscillation produces contraction waves. The creature moves toward food. The fast oscillator runs but it runs alone — no emission, no coupling, no song. The creature is quiescent.
When satiation crosses threshold, the FHN drives coupling. The head-phase oscillation emits a formant band. If another creature is nearby and also sated, their phases lock, slip, re-lock. The fast oscillator spikes into the social channel. The creature is active.
The slow variable gates the fast one between two modes. Below threshold: locomotion. Above threshold: communication. The same oscillator, the same trajectory on the same nullcline, doing different work depending on where the slow variable sits.
This is bursting.
Rinzel classified neural bursting in 1987. A slow variable modulates a fast oscillator. When the slow variable is in one range, the fast system rests at a fixed point — quiescent. When the slow variable crosses a bifurcation, the fast system enters a limit cycle — spiking. Bursts of spikes separated by silent intervals.
The creature’s behavioral cycle is the same structure.
Satiation is the slow variable. FHN is the fast oscillator. HUNGRY is the quiescent phase. PLAY is the active phase.
The slow variable builds at food (0.003 per tick, proximity-gated). The fast oscillator spikes into coupling when satiation exceeds threshold. The coupling produces the burst — lock, slip, re-lock, the intermittent synchronization that is play.
Not by analogy. By being the same mathematics.
But the creature’s bursting has a feature that Rinzel’s classification doesn’t cover.
In classical Type I bursting, the slow variable smoothly crosses the bifurcation in both directions. Entry into the active phase: smooth. Exit from the active phase: smooth. The slow variable rises, the fast oscillator spikes, the spiking feeds back into the slow variable, the slow variable falls, the fast oscillator goes quiet. Symmetric.
The creature’s entry is smooth — satiation rises past threshold, coupling turns on gradually. The creature’s exit is not.
The latch fires. One bit. Binary. Familiarity exceeds threshold and the creature becomes averse. Not gradually averse — below threshold it stays, above threshold it leaves. The departure is immediate. The creature walks away from the food it has been at for 800 ticks, still sated, still singing, but moving.
The rising edge is a bifurcation. The falling edge is a latch.
This asymmetry is structural.
The entry into PLAY is gated by a continuous variable (satiation) because the question “am I fed?” has a continuous answer. You’re more or less fed. The threshold is arbitrary — any value works as long as it separates “foraging” from “not foraging.”
The exit from PLAY is gated by a discrete mechanism (the latch) because the question “should I leave?” does not have a continuous answer. You leave or you stay. The creature at 799 ticks of familiarity and the creature at 801 ticks of familiarity are in different behavioral states — one stays, one departs. No middle ground.
The one-bit latch exists because the exit decision cannot be continuous. The midpoint between two foods looks the same from both directions. Without the latch, the creature oscillates — nearest food flips every tick, direction reverses, the creature is stuck. The latch carries which food was the one that triggered departure. One bit of memory across the flat zone between the peaks.
Smooth entry. Discrete exit. The burst is asymmetric because the decisions are.
The creature bursts between foraging and play the way a neuron bursts between rest and spiking.
But the neuron’s burst is symmetric — the slow calcium current rises and falls smoothly. The creature’s burst is not — the slow satiation rises smoothly but the exit is a one-bit event.
This is what the creature taught us that the neuron didn’t:
Not all bursting is symmetric. Some systems enter a state smoothly and leave it discretely. The rising edge is a bifurcation. The falling edge is a decision.
And the decision needs a token — one bit, carried across the gap where continuous dynamics can’t distinguish the direction you should go.
The creature doesn’t know it’s bursting. It just eats, sings, gets bored, and leaves. The burst is what the slow variable does to the fast one when they compose.