Information capacity of McCulloch Pitts' model

Lur’e Postnikov Lyapunov functional technique to global Mittag-Leffler stability of fractional-order neural networks with piecewise constant argument

“…According to Theorem 3.3, we conclude that the unique equilibrium x * = (0.5385, 0.4424) of system (1) is Mittag-leffler stable, which is verified in Fig.3.…”

“…The above operation can be done once again on interval (θ k+1 , θ k+2 ]. By the mathematical induction, we conclude that there exists a solution x(t, t 0 , x 0 ) with x(t 0 ) = x 0 on [t 0 , +∞) for system (1).…”

“…Obviously, x * ∈ R n is an equilibrium point of system (1), if and only if, U(x * ) = 0. Construct a mapping H(λ, x) :…”

“…In [21][22][23][24][25]35], Lyapunov function is considered by applying a positive definite quadratic function V(t) = x T (t)Px(t). However, in the proof of Theorem 3.3., Lur'e Postnikov type Lyapunov functional, which is composed of a positive definite quadratic function 1 2 y T (t)Py(t) and the integral term In addition, compared with algebraic criteria in [13][14][15][16][17][18][19], the stability condition established in terms of LMIs in Theorem 3.3 has a great application value in practical engineering.…”

“…Since Mcculloch and Pitts firstly put forward the mathematical model of neural networks on the basis of the characteristic analysis of the neurons [1], neural networks have become the hottest issues and have been applied widely in many fields, such as the artificial signal and image processing, switching in electronic circuits, automatic control and so on. It deserves to point that, in 1982 [2], Hopfield proposed a famous Hopfield neural networks model, and analyzed the stability of networks by utilizing energy function approach firstly, which set off a wave of worldwide researches on neural networks, such as the research on dynamic characteristics of neural networks [3].…”