A DELAYED CARBON–RENEWABLE–TEMPERATURE MODEL FOR TÜRKİYE USING PADOVAN COLLOCATION
16th International Azerbaijan Congress on Life, Engineering, Mathematical, and Applied Sciences |, Baku, Azerbaijan, 20 - 22 September 2026, pp.508-514, (Full Text)
- Publication Type: Conference Paper / Full Text
- City: Baku
- Country: Azerbaijan
- Page Numbers: pp.508-514
- Dokuz Eylül University Affiliated: Yes
Abstract
A reduced three-state nonlinear delay differential equation model is developed for the coupled dynamics
of carbon emissions, renewable-energy capacity, and temperature anomaly in Türkiye. The zero-delay
model is calibrated to published annual greenhouse-gas, renewable-capacity, and temperature data for
2000–2023, giving a positive renewable-substitution coefficient b = 0.0338 and physical-scale RMSE
values of 12.4 Mt, 0.60 GW, and 0.48 °C. In this reference case the high-renewable branch contains a
saddle near 401 Mt and a stable equilibrium near 683 Mt, which coalesce in a fold at bcrit = 0.0391;
alternative specifications indicate that this topology is calibration-sensitive. The stable upper
equilibrium is shown to be asymptotically stable for every non-negative delay, so that the delay affects
the transient approach but not the long-run state. The system is solved by piecewise collocation in a
Padovan-scaled monomial basis.