Payame Noor University (PNU) Control and Optimization in Applied Mathematics 2383-3130 2 2 2017 12 01 Global Asymptotic and Exponential Stability of Tri-Cell Networks with Different Time Delays پایداری مجانبی و نمایی سراسری شبکه های سه سلولی با تاخیرهای زمانی متفارت 45 60 5728 EN Zohreh Dadi Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord 94531, Iran Farzaneh Ravanbakhsh Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord 94531, Iran Journal Article 2018 10 31 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. https://mathco.journals.pnu.ac.ir/article_5728_d7d8ad7196d54741fba48dee2dc364e3.pdf