Computation of synchronized periodic solution in a BAM network with two delays

A bidirectional associative memory (BAM) neural network with four neurons and two discrete delays is considered to represent an analytical method, namely, perturbation-incremental scheme (PIS). The expressions for the periodic solutions derived from Hopf bifurcation are given by using the PIS. The result shows that the PIS has higher accuracy than the center manifold reduction (CMR) with normal form for the values of time delay not far away from the Hopf bifurcation point. In terms of the PIS, the necessary and sufficient conditions of synchronized periodic solution arising from a Hopf bifurcation are obtained and the synchronized periodic solution is expressed in an analytical form. It can be seen that theoretical analysis is in good agreement with numerical simulation. It implies that the provided method is valid and the obtained result is correct. To the best of our knowledge, the paper is the first one to introduce the PIS to study the periodic solution derived from Hopf bifurcation for a 4-D delayed system quantitatively.

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.

Stationary oscillation for chaotic shunting inhibitory cellular neural networks with impulses

In this paper, we study stationary oscillation for general shunting inhibitory cellular neural networks with impulses which are complex nonlinear neural networks. In a recent paper [Z. J. Gui and W. G. Ge, Chaos 16, 033116 (2006)], the authors claimed that they obtained a criterion of existence, uniqueness, and global exponential stability of periodic solution (i.e., stationary oscillation) for shunting inhibitory cellular neural networks with impulses. We point out in this paper that the main result of their paper is incorrect, and presents a sufficient condition of ensuring existence, uniqueness, and global stability of periodic solution for general shunting inhibitory cellular neural networks with impulses. The result is derived by using a new method which is different from those of previous literature. An illustrative example is given to demonstrate the effectiveness.

Global exponential periodicity and global exponential stability of a class of recurrent neural networks with various activation functions and time-varying delays

The paper presents theoretical results on the global exponential periodicity and global exponential stability of a class of recurrent neural networks with various general activation functions and time-varying delays. The general activation functions include monotone nondecreasing functions, globally Lipschitz continuous and monotone nondecreasing functions, semi-Lipschitz continuous mixed monotone functions, and Lipschitz continuous functions. For each class of activation functions, testable algebraic criteria for ascertaining global exponential periodicity and global exponential stability of a class of recurrent neural networks are derived by using the comparison principle and the theory of monotone operator. Furthermore, the rate of exponential convergence and bounds of attractive domain of periodic oscillations or equilibrium points are also estimated. The convergence analysis based on the generalization of activation functions widens the application scope for the model design of neural networks. In addition, the new effective analytical method enriches the toolbox for the qualitative analysis of neural networks.

Stochastic Exponential Stability for Markovian Jumping BAM Neural Networks With Time-Varying Delays

This correspondence provides stochastic exponential stability for Markovian jumping bidirectional associative memory neural networks with time-varying delays. An approach combining the Lyapunov functional with linear matrix inequality is taken to study the problems. Some criteria for the stochastic exponential stability are derived. The results obtained in this correspondence are less conservative, less restrictive, and more computationally efficient than the ones reported so far in the literature.

Stability and Hopf Bifurcation in a Simplified BAM Neural Network With Two Time Delays

Various local periodic solutions may represent different classes of storage patterns or memory patterns, and arise from the different equilibrium points of neural networks (NNs) by applying Hopf bifurcation technique. In this paper, a bidirectional associative memory NN with four neurons and multiple delays is considered. By applying the normal form theory and the center manifold theorem, analysis of its linear stability and Hopf bifurcation is performed. An algorithm is worked out for determining the direction and stability of the bifurcated periodic solutions. Numerical simulation results supporting the theoretical analysis are also given.

On the Almost Periodic Solution of Cellular Neural Networks With Distributed Delays

By exponential dichotomy about differential equations, a formal almost periodic solution (APS) of a class of cellular neural networks (CNNs) with distributed delays is obtained. Then, within different normed spaces, several sufficient conditions guaranteeing the existence and uniqueness of an APS are proposed using two fixed-point theorems. Based on the continuity property and some inequality techniques, two theorems insuring the global stability of the unique APS are given. Comparing with known literatures, all conclusions are drawn with slacker restrictions, e.g., do not require the integral of the kernel function determining the distributed delays from zero to positive infinity to be one, and the activation functions to be bounded, etc.; besides, all criteria are obtained by different ways. Finally, two illustrative examples show the validity and that all criteria are easy to check and apply.

New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay

In this letter, a new method is proposed for stability analysis of neural networks (NNs) with a time-varying delay. Some less conservative delay-dependent stability criteria are established by considering the additional useful terms, which were ignored in previous methods, when estimating the upper bound of the derivative of Lyapunov functionals and introducing the new free-weighting matrices. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

Global exponential stability of impulsive high-order BAM neural networks with time-varying delays

In this paper, global exponential stability and exponential convergence are studied for a class of impulsive high-order bidirectional associative memory (BAM) neural networks with time-varying delays. By employing linear matrix inequalities (LMIs) and differential inequalities with delays and impulses, several sufficient conditions are obtained for ensuring the system to be globally exponentially stable. Three illustrative examples are also given at the end of this paper to show the effectiveness of our results.

Global point dissipativity of neural networks with mixed time-varying delays

By employing the Lyapunov method and some inequality techniques, the global point dissipativity is studied for neural networks with both discrete time-varying delays and distributed time-varying delays. Simple sufficient conditions are given for checking the global point dissipativity of neural networks with mixed time-varying delays. The proposed linear matrix inequality approach is computationally efficient as it can be solved numerically using standard commercial software. Illustrated examples are given to show the usefulness of the results in comparison with some existing results.