Analysis methods for neutral delay differential equations

GRISELDA R. ITOVICH; FRANCO S. GENTILE; JORGE L. MOIOLA

Bahia Blanca

Congreso; XVIII Reunión de trabajo en Procesamiento de la Información y Control; 2019

Instituto de Investigaciones en Ingenieria Electrica "Alfredo Desages" -IIIE (UNS-CONICET)

Two different methods for the stability and bifurcation analyses of neutral delay differential equations are presented. The first one relies on classical techniques and it is oriented to the study of the roots of the characteristic equation, which is a transcendental one. It provides a straightforward test to obtain the stability chart in the parameter space of the studied system. The second method uses a frequency-domain approach, based on the control theory, to determine the stability and dynamic bifurcations, and also providing approximations for the smooth oscillations appearing when the system loses its stability.