Multiple Lagrange stability and Lyapunov asymptotical stability of delayed fractional-order Cohen-Grossberg neural networks

This paper addresses the coexistence and local stability of multiple equilibrium points for fractional-order Cohen-Grossberg neural networks(FOCGNNs)with time delays.Based on Brouwer's fixed point theorem,sufficient conditions are established to ensure the existence of Πi=1^n(2Ki+1)equilibrium points for FOCGNNs.Through the use of Hardy inequality,fractional Halanay inequality,and Lyapunov theory,some criteria are established to ensure the local Lagrange stability and the local Lyapunov asymptotical stability of Πi=1^n(Ki+1)equilibrium points for FOCGNNs.The obtained results encompass those of integer-order Hopfield neural networks with or without delay as special cases.The activation functions are nonlinear and nonmonotonic.There could be many corner points in this general class of activation functions.The structure of activation functions makes FOCGNNs could have a lot of stable equilibrium points.Coexistence of multiple stable equilibrium points is necessary when neural networks come to pattern recognition and associative memories.Finally,two numerical examples are provided to illustrate the effectiveness of the obtained results.

Coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions

In this paper, coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions are addressed. Because of the discontinuity of the activation function, Filippov solution of the neural network is defined. Based on Brouwer's fixed point theorem and definition of Mittag–Leffler stability, sufficient criteria are established to ensure the existence of (2k + 3)~n (k ≥ 1) equilibrium points, among which (k + 2)~n equilibrium points are locally Mittag–Leffler stable. Compared with the existing results, the derived results cover local Mittag–Leffler stability of both fractional-order and integral-order recurrent neural networks. Meanwhile discontinuous networks might have higher storage capacity than the continuous ones. Two numerical examples are elaborated to substantiate the effective of the theoretical results.

A Locating Method for Reliability-Critical Gates with a Parallel-Structured Genetic Algorithm

The reliability allowance of circuits tends to decrease with the increase of circuit integration and the application of new technology and materials, and the hardening strategy oriented toward gates is an effective technology for improving the circuit reliability of the current situations. Therefore, a parallel-structured genetic algorithm (GA), PGA, is proposed in this paper to locate reliability-critical gates to successfully perform targeted hardening. Firstly, we design a binary coding method for reliability-critical gates and build an ordered initial population consisting of dominant individuals to improve the quality of the initial population. Secondly, we construct an embedded parallel operation loop for directional crossover and directional mutation to compensate for the deficiency of the poor local search of the GA. Thirdly, for combination with a diversity protection strategy for the population, we design an elitism retention based selection method to boost the convergence speed and avoid being trapped by a local optimum. Finally, we present an ordered identification method oriented toward reliability-critical gates using a scoring mechanism to retain the potential optimal solutions in each round to improve the robustness of the proposed locating method. The simulation results on benchmark circuits show that the proposed method PGA is an efficient locating method for reliability-critical gates in terms of accuracy and convergence speed.