Resumen de Positivity and stability of coupled differential–difference equations with time-varying delays
This paper studies the asymptotic stability of a special class of coupled delay differential–difference equations with internal positive property. An explicit characterization on the positivity of coupled differential–difference equations is firstly given. Then, based on the positivity of coupled differential–difference equations with constant delays, we investigate the entrywise monotonicity and asymptotic property of their state trajectories starting from appropriately chosen initial conditions. Furthermore, the time-varying delay system is analyzed through comparing with the corresponding constant delay system. It turns out that an internally positive coupled differential–difference equation with bounded time-varying delays is asymptotically stable as long as the corresponding delay-free system is asymptotically stable.
