Global asymptotic stability of nonautonomous Cohen–Grossberg neural network models with infinite delays

Abstract

a b s t r a c tFor a general Cohen-Grossberg neural network model with potentially unbounded timevarying coefficients and infinite distributed delays, we give sufficient conditions for its global asymptotic stability. The model studied is general enough to include, as subclass, the most of famous neural network models such as Cohen-Grossberg, Hopfield, and bidirectional associative memory. Contrary to usual in the literature, in the proofs we do not use Lyapunov functionals. As illustrated, the results are applied to several concrete models studied in the literature and a comparison of results shows that our results give new global stability criteria for several neural network models and improve some earlier publications.

Equilibrium and Stability Analysis of Takagi-Sugeno Fuzzy Delayed Cohen-Grossberg Neural Networks

“…which is of the form jg T (z)j( )jg(z)j 0 or equivalently jg T (z)j jg(z)j 0: On the other hand, if is a positive de…nite matrix, then, for all g(z(t)) 6 = 0, we have jg T (z)j jg(z)j > 0: Obviously, when > 0, (14) contradicts with (15), implying that under the condition of Theorem 1, the equilibrium equation of system (5) given by (6) cannot have a solution where g(z) 6 = 0. Thus, we can conclude that Theorem 1 guarantees that the origin of system (5) is the unique equilibrium point.…”

“…We will prove this theorem by using the contradiction method. Let z 6 = 0 be an equilibrium point of system (5). Then, we have…”

“…In this section, we will present two main theorems. The …rst theorem proves the uniqueness of equilibrium point for system (5), which is stated as follows : ; m such that the following condition holds :…”

“…Remark 3. In [21]- [38], the stability of fuzzy neural system (5) have been established by using the LMI (linear matrix inequality approach) or the M-matrix based approach. It should be pointed out here that stability conditions expressed in the LMI forms need to be checked for negative de…niteness of the high dimensional matrices formed by network parameters of neural systems.…”

Global exponential stability of discrete-time Hopfield neural network models with unbounded delays

“…Using systems with unbounded delay, it is possible to modulate phenomena where the entire history affects the present. At this time, the continuous-time neural network model with unbounded delay is widely studied (see [5,12,19,25,36] and references therein), while few research works are focus on the discrete-time case [6]. To the best of our knowledge, the global stability of a discrete-time high-order neural network model with unbounded delay has not been studied yet.…”