Global Asymptotic and Exponential Stability of Tri-Cell Networks with Different Time Delays

In this paper‎, ‎a bidirectional ring network with three cells and different time delays is presented‎. ‎To propose this model which is a good extension of three-unit neural networks‎, ‎coupled cell network theory and neural network theory are applied‎. ‎In this model‎, ‎every cell has self-connections without delay but different time delays are assumed in other connections‎. ‎A suitable Lyapunov function is presented for this model which helps to get sufficient conditions to guarantee asymptotic and exponential stability of the model‎. ‎Also‎, ‎these conditions are independent of time delays‎. ‎Finally‎, ‎analytical results are confirmed by numerical examples which are stated.

Keywords:

Asymptotic ‎stability‎ , Exponential stability , Nonlinear systems , Cell network