In this paper, some sufficient conditions for the local and global exponential stability of the discrete-time Hopfield neural networks with general activation functions are derived, which generalize those existing results. By means of Mmatrix theory and some inequality analysis techniques, the exponential convergence rate of the neural networks to the equilibrium is estimated, and for the local exponential stability, the basin of attraction of the stable equilibrium is also characterized. © 2004 Elsevier Ltd. All rights reserved.

We consider a delayed network of two neurons with both self-feedback and interaction described by an all-or-none threshold function. The model describes a combination of analog and digital signal processing in the network and takes the form of a system of delay differential equations with discontinuous nonlinearity.We show that the dynamics of the network can be understood in terms of the iteration of a one-dimensional map, and we obtain simple criteria for the convergence of solutions, the existence, multiplicity and attractivity of periodic solutions. © 2005 Elsevier B.V. All rights reserved.

In this paper, we study a class of neural networks, which includes bidirectional associative memory networks and cellular neural networks as its special cases. By Brouwer's fixed point theorem, a continuation theorem based on Gains and Mawhin's coincidence degree, matrix theory, and inequality analysis, we not only obtain some different sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the equilibrium but also estimate the exponentially convergent rate. Our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity.

A parallel-plate capacitance-based sensor configuration which can be used to measure low mass concentrations down to a few tens of g/m3 for gas-particle systems and to study the influence of the particle characteristics such as particle size, packing or agglomeration on the effective permittivity of the mixture was developed. In this sensor a two channel symmetric structure and an AC bridge circuit were adopted to minimise the influence from the surrounding factors such as temperature, pressure and humidity. The inner diameter of the flow pipeline is 18mm, the dimension of the capacitance plate is 100mm 50mm and the distance of the two plates is 10mm. To measure the concentration of particles an in situ two-step measurement was proposed, i.e. zero point and loading measurements. Emphasis was made on estimation of the static and dynamic performance of the capacitance sensor and configuration. The baseline drift of the sensor and the influence of surrounding factors were studied. Dynamic experiments show a relative measurement error of 8% in the range from 10 to 300g/m3. Static experiments for locally packed particle-gas systems show that the response of the sensor depends not only on particle material but also on particle size.

In this Letter, we study BAM (bidirectional associative memory) networks with variable coefficients. By some spectral theorems and a continuation theorem based on coincidence degree, we not only obtain some new sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the periodic solution but also estimate the exponentially convergent rate. Our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity. Moreover, these conclusions are presented in terms of system parameters and can be easily verified for the globally Lipschitz and the spectral radius being less than 1. Therefore, our results should be useful in the design and applications of periodic oscillatory neural circuits for neural networks with delays. © 2003 Elsevier B.V. All rights reserved.