Catálogo de publicaciones - libros

The paper investigates the existence and global stability of periodic solution of non-autonomous neural networks with delay. Then the existence and uniqueness of periodic solutions of the neural networks are discussed in the paper. Moreover, criterion on stability of periodic solutions of the neural networks is obtained by using matrix function inequality, and algorithm for the criterion on the neural networks is provided. Result in the paper generalizes and improves the result in the existing references. In the end, an illustrate example is given to verify our results.

In this paper, a class of generalized nonautonomous cellular neural networks with time-varying delays are studied. By means of Lyapunov functional method, improved Young inequality  ≤  +  (0 ≤  ≤ 1,  +  = 1, > 0) and the homeomorphism theory, several sufficient conditions are given guaranteeing the existence, uniqueness and global exponential stability of the equilibrium point. The proposed results generalize and improve previous works. An illustrative example is also given to demonstrate the effectiveness of the proposed results.

The global asymptotic stability of discrete-time Cohen–Grossberg neural networks (CGNNs) with or without time delays is studied in this paper. The CGNNs are transformed into discrete-time interval systems, and several sufficient conditions of asymptotic stability for these interval systems are derived by constructing some suitable Lyapunov functionals. The obtained conditions are given in the form of linear matrix inequalities that can be checked numerically and very efficiently by resorting to the MATLAB LMI Control Toolbox.

In this paper, the global asymptotic and exponential stability are investigated for a class of neural networks with distributed time-varying delays. By using appropriate Lyapunov-Krasovskii functional and linear matrix inequality (LMI) technique, two delay-dependent sufficient conditions in LMIs form are obtained to guarantee the global asymptotic and exponential stability of the addressed neural networks. The proposed stability criteria do not require the monotonicity of the activation functions and the differentiability of the distributed time-varying delays, which means that the results generalize and further improve those in the earlier publications. An example is given to show the effectiveness of the obtained condition.

In finite mixture modelling, it is crucial to select the number of components for a data set. We have proposed an entropy regularized likelihood (ERL) learning principle for the finite mixtures to solve this model selection problem under regularization theory. In this paper, we further give an asymptotic analysis of the ERL learning, and find that the global minimization of the ERL function in a simulated annealing way (i.e., the regularization factor is gradually reduced to zero) leads to automatic model selection on the finite mixtures with a good parameter estimation. As compared with the EM algorithm, the ERL learning can go across the local minima of the negative likelihood and keep robust with respect to initialization. The simulation experiments then prove our theoretic analysis.

The existence and global asymptotic stability of a large class of Cohen-Grossberg neural networks is discussed in this paper. Previous papers always assume that the amplification function has positive lower and upper bounds, which excludes a large class of functions. In our paper, it is only needed that the amplification function is positive. Also, the model discussed is general, the method used is direct and the conditions needed are weak.

This paper studies a general class of neural networks with time-varying delays and the neuron activations belong to the set of discontinuous monotone increasing functions. The discontinuities in the activations are an ideal model of the situation where the gain of the neuron amplifiers is very high. Because the delay in combination with high-gain nonlinearities is a particularly harmful source of potential instability, in the paper, conditions which ensure the global convergence of the neural network are derived.

In this paper, the difference between using the inverted neuron output and negative resistor for expressing inhibitory synapse is studied. We analyzed that the total conductance seen at the neuron input is different in these two methods. And this total conductance has been proved to effect on the system stability in this paper. Also, we proposed the method how to stabilize the input space and improve the system’s performance by adjusting the input conductance between neuron input and ground. Pspice is used for circuit level simulation.

In this paper, we investigate dynamical behavior of a general class of competitive or cooperative Lotka-Volterra systems with delays. Positive solutions and global stability of nonnegative equilibrium are discussed. Sufficient condition independent of delays guaranteeing existence of globally stable equilibrium is given. A Simulation verifying theoretical results is given, too.

Discrete-time analogues of continuous-time neural networks with continuously distributed delays and periodic inputs are introduced. The discrete-time analogues are considered to be numerical discretizations of the continuous-time networks and we study their dynamical characteristics. By employing Halanay-type inequality, we obtain easily verifiable sufficient conditions ensuring that every solutions of the discrete-time analogue converge exponentially to the unique periodic solutions. It is shown that the discrete-time analogues preserve the periodicity of the continuous-time networks.