Summary
Delay differential equations (DDEs) have been employed to investigate the El Niño Southern Oscillation (ENSO) phenomenon. This type of conceptual model typically involves a delayed negative feedback term and a nonautonomous periodic forcing. Despite their simplicity, recent studies have revealed that such DDE models exhibit intricate dynamical behavior, especially in cases where delays are not assumed to be constant. Our starting point is an idealized DDE ENSO model in which the negative delayed feedback term is represented by a step function with constant delay. We expand upon previous work on this model by incorporating state-dependent delays, while keeping the step function to enable us to construct explicit solutions. Specifically, we show that the constant delay case serves as an accurate approximation for a family of implicitly defined state-dependent delays.
