Periodic solutions and exponential stability in delayed cellular neural networks

Global exponential stability of bidirectional associative memory neural networks with time delays

In this paper, we consider delayed bidirectional associative memory (BAM) neural networks (NNs) with Lipschitz continuous activation functions. By applying Young's inequality and Hoelder's inequality techniques together with the properties of monotonic continuous functions, global exponential stability criteria are established for BAM NNs with time delays. This is done through the use of a new Lyapunov functional and an M-matrix. The results obtained in this paper extend and improve previous results.

Existence and Global Exponential Stability of Almost Periodic Solution for Cellular Neural Networks With Variable Coefficients and Time-Varying Delays

In this paper, we study cellular neural networks with almost periodic variable coefficients and time-varying delays. By using the existence theorem of almost periodic solution for general functional differential equations, introducing many real parameters and applying the Lyapunov functional method and the technique of Young inequality, we obtain some sufficient conditions to ensure the existence, uniqueness, and global exponential stability of almost periodic solution. The results obtained in this paper are new, useful, and extend and improve the existing ones in previous literature.

Global Asymptotic Stability Analysis of Bidirectional Associative Memory Neural Networks With Time Delays

This paper presents a sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for bidirectional associative memory (BAM) neural networks with distributed time delays. The results impose constraint conditions on the network parameters of neural system independently of the delay parameter, and they are applicable to all continuous nonmonotonic neuron activation functions. It is shown that in some special cases of the results, the stability criteria can be easily checked. Some examples are also given to compare the results with the previous results derived in the literature.

Global eponential stability of cellular neural networks with time-varying coefficients and delays

In this paper, a class of cellular neural networks with time-varying coefficients and delays is considered. By constructing a suitable Liapunov functional and utilizing the technique of matrix analysis, some new sufficient conditions on the global exponential stability of solutions are obtained. The results obtained in this paper improve and extend some of the previous results.

An analysis of exponential stability of delayed neural networks with time varying delays

This paper derives a new sufficient condition for the exponential stability of the equilibrium point for delayed neural networks with time varying delays by employing a Lyapunov-Krasovskii functional and using Linear Matrix Inequality (LMI) approach. This result establishes a relation between the delay time and the parameters of the network. The result is also compared with the most recent result derived in the literature.

Bifurcation analysis and existence of periodic solutions in a simple neural network with delays

Results are provided here about the stability and bifurcation of periodic solutions for a (neural) network with n elements where delays between adjacent units and external inputs are included. The particular cases n = 2 and n = 3 are discussed in details, to explicitly illustrate the role of the delays in the corresponding bifurcation sets and the stability properties, like a Hopf bifurcation, a pitchfork bifurcation, and a Bogdanov-Takens bifurcation.

Boundedness and stability for nonautonomous cellular neural networks with delay

In this paper, a class of nonautonomous cellular neural networks is studied. By constructing a suitable Liapunov functional, applying the boundedness theorem for general functional-differential equations and the Banach fixed point theorem, a series of new criteria are obtained on the boundedness, global exponential stability, and existence of periodic solutions.

Global stability of neural networks with distributed delays

In this paper, a model describing the dynamics of recurrent neural networks with distributed delays is considered. Some sufficient criteria are derived ensuring the global asymptotic stability of distributed-delay recurrent neural networks with more general signal propagation functions by introducing real parameters p>1, q(ij)>0, and r(jj)>0, i,j=1, em leader,n, and applying the properties of the M matrix and inequality techniques. We do not assume that the signal propagation functions satisfy the Lipschitz condition and do not require them to be bounded, differentiable, or strictly increasing. Moreover, the symmetry of the connection matrix is also not necessary. These criteria are independent of the delays and possess infinitely adjustable real parameters, which is important in signal processing, especially in moving image treatment and the design of networks.

Exponential stability and periodic solutions of neural networks with continuously distributed delays

In this paper we study a class of neural networks with continuously distributed delays. By means the of Lyapunov functional method, we obtain some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the equilibrium and periodic solution. We 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. Therefore, our results play an important role in the design of globally exponentially stable neural circuits and periodic oscillatory neural circuits.

Global exponential stability and periodic solutions of cellular neural networks with delay

In this paper, some sufficient conditions for the global exponential stability and the existence of periodic solutions of cellular neural networks with delay (DCNN) model are obtained by means of a Lyapunov functional approach. These conditions can be used to design globally stable DCNN's and periodic oscillatory DCNN's and thus have important significance in both theory and applications.