Separation Anxiety Stress Timeline (2D)

Absence Setup

Absence duration 30 min

How long the owner is gone this cycle. Longer absences let stress climb closer to its ceiling before the cycle ends.

Playback speed 1.0×

Departure training

Enrichment (toy / audio)

Live Stress Readout

LEAVING

Time alone

0:00

Stress level

Peak this cycle

Stress ceiling

95%

Rise time constant (τ)

2.5 min

Practice openings

How it works — the stress-response curve

Stress is modeled as rising from 0 toward a ceiling on an exponential curve set by a time constant τ: stress(t) = ceiling × (1 − e^(−t/τ)), where t is minutes alone. A high ceiling and a short τ mean the dog reaches near-panic quickly; a lower ceiling and a longer τ mean the rise is slower and shallower.

Departure training (graduated desensitization) lowers the ceiling by 0.32 and lengthens τ by 4.5 minutes — both a lower peak and a slower climb. It also unlocks brief "practice" door-openings during the absence, each producing a short dip in the timeline, mirroring short low-stakes departures used in real training.
Enrichment (a stuffed puzzle toy, calming audio, worn owner clothing) lowers the ceiling by 0.18 and lengthens τ by 1.5 minutes, independent of training.
Once stress passes 25%, small oscillation bursts are added on top of the curve — the bouts of barking or howling that come in waves rather than a smooth ramp.
On return, stress decays rapidly back toward zero as the reunion phase plays out.

Stress curve Practice opening Ceiling