Without assuming boundedness and differentiability of the activation functions and any symmetry of interconnections, we employ Lyapunov functions to establish some sufficient conditions ensuring existence, uniqueness, global asymptotic stability, and even global exponential stability of equilibria for the Cohen–Grossberg neural networks with and without delays. Our results are not only presented in terms of system parameters and can be easily verified and also less restrictive than previously known criteria and can be applied to neural networks, including Hopfield neural networks, bidirectional association memory neural networks, and cellular neural networks.

We study the existence and branching patterns of wave trains in the one-dimensional in nite Fermi-Pasta-Ulam (FPU) lattice. A wave train Ansatz in this Hamiltonian lattice leads to an advance-delay di erential equation on a space of periodic functions, which carries a natural Hamiltonian structure. The existence of wave trains is then studied by means of a Lyapunov Schmidt reduction, leading to a nite-dimensional bifurcation equation with an inherited Hamiltonian structure. While exploring some of the additional symmetries of the FPU lattice, we use invariant theory to nd the bifurcation equations describing the branching patterns of wave trains near p∶q resonant waves. We show that at such branching points, a generic nonlinearity selects exactly two two-parameter families of mixed-mode wave trains.

In this paper, we study a class of neural networks with variable coefficients which includes delayed Hopfield neural networks, bidirectional associative memory networks and cellular neural networks as its special cases. By matrix theory and inequality analysis, we not only obtain some new sufficient conditions ensuring the existence, uniqueness, global attractivity 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 have an important leading significance in the design and applications of periodic oscillatory neural circuits for neural networks with delays. © 2005 Elsevier Ltd. All rights reserved.

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 paper, we consider a simple discrete two-neuron network model with three delays. The characteristic equation of the linearized system at the zero solution is a polynomial equation involving very high order terms. We derive some sufficient and necessary conditions on the asymptotic stability of the zero solution. Regarding the eigenvalues of connection matrix as the bifurcation parameters, we also consider the existence of three types of bifurcations: Fold bifurcations, Flip bifurcations, and Neimark-Sacker bifurcations. The stability and direction of these three kinds of bifurcations are studied by applying the normal form theory and the center manifold theorem. Our results are a very important generalization to the previous works in this field. © 2007 Published by Elsevier Ltd.