CBT Thought–Emotion Feedback Loop

Trigger an Automatic Thought

Trigger intensity 0.60

Cognitive distortion

Feedback loop coupling 1.00×

System at rest.

Loop State

Distress (Emotion)

0.00

Arousal (Physiology)

0.00

Avoidance (Behavior)

0.00

Loop gain (spectral r)

0.00

How it works

CBT's "hot cross bun" formulation models a mental-health episode as four coupled nodes — Thought (T), Emotion (E), Physiology (P), Behavior (B) — that reinforce each other in a vicious cycle. Each node relaxes toward zero on its own but is pushed up by the others:

dT/dt = -k·T + input(t)
dE/dt = -k·E + g·(w_TE·T + w_PE·P + w_BE·B)
dP/dt = -k·P + g·(w_TP·T + w_EP·E)
dB/dt = -k·B + g·(w_TB·T + w_EB·E)

g is the coupling slider — the strength of the vicious cycle. Each distortion preset changes which weights w dominate (catastrophizing drives T→P hardest; mind-reading and all-or-nothing drive T→E; overgeneralization drives T→B avoidance). The loop gain readout is the coupling matrix's spectral radius: below 1 the system self-extinguishes, at/above 1 it amplifies — the mathematical signature of a spiral.

CBT reframing is simulated as a real intervention on the equations, not a cosmetic reset: it temporarily cuts the Thought→Emotion weight (cognitive restructuring — the thought is challenged before it can drive feeling) and adds direct damping to E (behavioral/somatic coping), which collapses the loop gain below 1 and lets the whole system decay back to baseline exponentially, exactly as CBT is theorized to work clinically.

Trigger — injects an automatic negative thought impulse of the chosen intensity into T.
Coupling — how strongly the four nodes reinforce each other (the "vicious cycle" strength).
Reframe — applies an 8-second cognitive-restructuring intervention: weakened T→E coupling + direct emotional damping.

Thought Emotion Physiology Behavior

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CBT Thought–Emotion Feedback Loop Simulator