2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/208710A nonlinear differential equation of Sornette-Ide type with noise, for a complex variable, yields endogenous crashes, preceded by roughly log-periodic oscillations in the real part, and a strong increase in the imaginary part. The latter is interpreted as the trader expectation.4 pages including two figures, for Int. J. Mod. Phys. C 14, issue 4 (2002)Statistical MechanicsTrading and Market Microstructuretext