Estimating the region of attraction of integral delay equations

Abstract We present estimates of the region of attraction of a class of non-linear integral delay equations. The approach follows the same lines as the Lyapunov method by the first approximation for estimating the attraction region of ordinary and delay differential equations, which uses Lyapunov functions or Lyapunov functionals associated with the linear part of the non-linear equations. The results are illustrated by application problems to the propagation of electric pulses in the heart dynamics and non-linear predictor control.