Haijun Jiang

Existence and global exponential stability of equilibrium of competitive neural networks with different time scales and multiple delays

Abstract In this paper, some sufficient conditions are obtained for existence and global exponential stability of a unique equilibrium point of competitive neural networks with different time scales and multiple delays by using nonlinear Lipschitz measure (NLM) method and constructing suitable Lyapunov functional. The results of this paper are new and they complete previously known results.

Existence and globally exponential stability of periodic solution of BAM neural networks with impulses and recent-history distributed delays

In this paper, a class of generalized bi-directional associative memory (BAM) neural networks with recent history distributed delays and impulses are considered. By using Lyapunov functional method and fixed point theorem, we derive several sufficient conditions for the existence and globally exponential stability of a unique periodic solution of the networks. The results of this paper are new and different from previously known results.

Exponential stability and periodic solutions of FCNNs with variable coefficients and time-varying delays

In this paper, we investigate the fuzzy cellular neural networks (FCNNs) with variable coefficients and time-varying delays. A series of simple sufficient conditions is obtained for checking the boundedness, global exponential stability and the existence and global exponential stability of periodic solutions of FCNNs with variable coefficients and time-varying delays by using Young inequality and general Lyapunov functional. The results given in this paper extend and improve the earlier publications.

Robust stochastic stability analysis of Markovian switching genetic regulatory networks with discrete and distributed delays

In this paper, we investigate robust stochastic stability of Markovian switching genetic regulatory networks with discrete and distributed delays. Different from previous correspondingly works, discrete and distributed delays are involved to describe the concentration of macromolecule for genetic networks. Based on the Lyapunov stability theory and linear matrix inequality (LMI), sufficient conditions are given to ensure the stability in the mean square of the stochastic genetic networks with Markovian switching. An illustrative example is given to show the effectiveness of our theoretical results.

On the distribution of the roots of a fifth degree exponential polynomial with application to a delayed neural network model

In this paper, we mainly study the distribution of the roots of a fifth degree exponential polynomial. We obtain the sufficient and necessary conditions for the existence of purely imaginary roots of the exponential polynomial. Applying the obtained results, we consider a neural network model consisting of five neurons with delays. The sum of delays @t is regarded as the bifurcation parameter. Under some conditions, we show that the zero solution is locally asymptotically stable when the time delay is suitably small, while change of stability of zero solution will cause a bifurcating periodic solution as the time delay @t passes through a certain critical value. In order to illustrate our theoretical analysis, some numerical simulations are presented.

Boundedness and exponential stability for nonautonomous FCNNs with distributed delays and reaction-diffusion terms

In this paper, the boundedness and exponential stability for nonautonomous fuzzy cellular neural networks (FCNNs) with distributed delays and reaction-diffusion terms are investigated. By constructing suitable Lyapunov functional, introducing ingeniously some real parameters and applying the elementary inequality, we establish a series of criteria on the boundedness and globally exponential stability of solutions. In these criteria, we do not require that the response functions are bounded and differentiable. Finally, an example is given to show the effectiveness of the obtained results.

The boundedness of high-order Hopfield neural networks with variable delays

In this paper, the uniformly boundedness and uniformly ultimately boundedness of high-order neural networks with time-varying delays are studied. Proper Lyapunov functionals and some analytic techniques are employed to derive the sufficient conditions under which the networks proposed are uniformly bounded and uniformly ultimately bounded. The results are shown to improve the results derived in [1] (Arik, 2004). Some examples are given to illustrate the correctness of our results.

PERIODICITY AND STABILITY IN RECURRENT CELLULAR NEURAL NETWORKS WITH IMPULSIVE EFFECTS

In this paper, the exponential stability analysis problem is considered for a class of impulsive recurrent cellular neural networks (IRCNNs) with time-varying delays. Without assuming the boundedness on the activation functions, some sufficient conditions are derived for checking the existence and exponential stability of periodic solution for this system by using Mawhins continuation theorem of coincidence degree theory and constructing suitable Lyapunov functional. It is believed that these results are significant and useful for the design and applications of IRCNNs. Finally, an example with numerical simulation is given to show the effectiveness of the proposed method and results.

BOUNDEDNESS AND EXPONENTIAL STABILITY FOR NONAUTONOMOUS FCNNs WITH REACTION-DIFFUSION TERMS AND TINE-VARYING DELAYS

In this paper, a class of nonautonomous fuzzy cellular neural networks (FCNNs) with reaction-diffusion terms and time-varying delays are investigated. By applying the inequality analysis technique, introducing ingeniously many real parameters and constructing new auxiliary functions, a series of new and useful criteria on the boundedness and globally exponential stability of solutions are established. The results obtained in this paper extend and improve the corresponding results given in previous works. Finally, two examples are given to verify the effectiveness of the obtained results.

Dynamics of solution for a class of delayed diffusive neural networks with mixed boundary conditions

In this paper, we investigate a class of cellular neural networks model with delays and diffusive terms. By using the method of upper and lower solutions, we obtain that if the neuronal output signal functions in system possess mixed quasimonotone property and the corresponding elliptic system has upper and lower solutions the model has a unique nonconstant equilibrium solution. Under some additional conditions we further obtain that the solution of the neural networks converges to this nonconstant equilibrium solution.