Positive feedback creates bistability and hysteresis. Negative feedback creates adaptation and oscillations. Phase plane, time series, and bifurcation diagram.
Feedback type
x: 0
y: 0
Mode: bistable
Time series
Bifurcation diagram (x vs S)
Positive feedback (PFB): activation promotes further activation. Creates bistability: two stable steady states (off and on) with a threshold. Cells can "commit" to a fate irreversibly (e.g. CDK1 in mitosis, Ras in differentiation). Hysteresis: the state depends on history — the system switches on at one threshold but doesn't switch off until a lower threshold. Negative feedback (NFB): activation promotes its own inhibition. Creates adaptation (output returns to baseline despite persistent input) and can generate oscillations (Goodwin 1965). Phase plane: nullclines (dx/dt=0, dy/dt=0) intersect at steady states; arrows show flow; limit cycles appear for oscillatory NFB.