Global stability analysis of bidirectional associative memory neural networks with time delay

Abstract

SUMMARYIn this paper, without assuming the boundedness, monotonicity and di erentiability of the activation functions, we present new conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of bidirectional associative memory neural networks with ÿxed time delays or distributed time delays. The results are applicable to both symmetric and non-symmetric interconnection matrices, and all continuous non-monotonic neuron activation functions.

Absolute stability of a class of neural networks with unbounded delay

“…When neural networks contain ÿxed time delays or only unbounded time delay, researchers analyse the stability of the neural networks by constructing proper scale Liapunov functionals or functions [4,5,[9][10][11][12][13][14][15][16][17][18][20][21][22]. However, if neural networks contain both variable time delays and unbounded time delay, then the mathematical methods in those papers cannot be applied.…”

“…Gopalsamy and He [16] studied the asymptotical stability of Hopÿeld-type neural networks involving unbounded time delay arising from the signal propagation. Some results on the stability of neural networks involving unbounded time delays are given in References [16][17][18][19][20][21]. Though delays arise frequently in practical applications, it is di cult to measure them precisely.…”

On input-to-state stability for stochastic coupled control systems on networks

“…[1][2][3][4]. Stability analysis for coupled control systems on networks is one of the most important problems in control theory and engineering [5][6][7][8]. However, coupled control systems on networks in many applications are often perturbed by environmental noise in the real world.…”

Integro-differential inequality and stability of BAM FCNNs with time delays in the leakage terms and distributed delays

“…Therefore, study of neural dynamics with consideration of the delayed problem becomes extremely important to manufacture high-quality neural networks. In recent years, there have been many analytical results for BAM neural networks with various axonal signal transmission delays, for example, see [3][4][5][6][7][8][9][10][11] and references therein. In addition, except various axonal signal transmission delays, time delay in the leakage term also has great impact on the dynamics of neural networks.…”