This page integrates a single scalar delay differential equation intended as a cartoon of the “delayed oscillator” mechanism discussed for ENSO: a positive delayed feedback a·x(t−τ) represents ocean adjustment communicating past sea-surface warmth back to the atmosphere, while −b·x provides damping and −c·x³ limits amplitude. An optional slow sinusoidal forcing mimics seasonal modulation. The full Suarez–Schopf (1988) model is a coupled ocean–atmosphere PDE system; here only the reduced feedback story is retained so students can tune τ, a, and forcing to see periodic or irregular warm/cool swings analogous to El Niño / La Niña in name only.
Who it's for: Climate dynamics or applied ODE courses introducing interannual variability.
Key terms
ENSO
Delayed oscillator
Suarez–Schopf
El Niño
La Niña
DDE
Suarez & Schopf (1988) coupled ocean–atmosphere instabilities in a full model; here you get the reduced story: delayed signal + damping + nonlinearity + optional annual cycle.
Live graphs
Phase plot uses the same τ as the integrator; limit cycles suggest repeating warm/cool swings analogous to El Niño / La Niña episodes in toy form.
How it works
A one-variable delay differential equation with seasonal forcing illustrates how ocean adjustment lag plus Bjerknes-style feedback can produce irregular oscillations reminiscent of ENSO — a schematic delayed oscillator, not a coupled GCM.
Frequently asked questions
Is x the Niño-3.4 index?
No. x is a dimensionless anomaly with no calibration to observations; labels are qualitative only.
Why not implement the original Suarez–Schopf equations?
Their intermediate complexity (spatial structure, many parameters) hides the core delayed-feedback loop that this toy isolates.