Global Mittag-Leffler Boundedness for Fractional-Order Complex-Valued Cohen–Grossberg Neural Networks

Since the origins of artificial neural network research, many models of feedforward networks have been proposed. This paper presents an algorithm which adapts the shape of the activation function to the training data, so that it is learned along with the connection weights. The activation function is interpreted as a piecewise polynomial approximation to the distribution function of the argument of the activation function. An online learning procedure is given, and it is formally proved that it makes the training error decrease or stay the same except for extreme cases. Moreover, the model is computationally simpler than standard feedforward networks, so that it is suitable for implementation on FPGAs and microcontrollers. However, our present proposal is limited to two-layer, one-output-neuron architectures due to the lack of differentiability of the learned activation functions with respect to the node locations. Experimental results are provided, which show the performance of the proposal algorithm for classification and regression applications.     

An Analysis of Global Stability of Takagi–Sugeno Fuzzy Cohen–Grossberg Neural Networks with Time Delays

Neural Processing Letters - This paper deals with the problem of the global asymptotic stability of Takagi–Sugeno (T–S) fuzzy Cohen–Grossberg neural networks with multiple time...     

New Results for Exponential Synchronization of Memristive Cohen–Grossberg Neural Networks with Time-Varying Delays

Neural Processing Letters - This paper concerns the topic of exponential synchronization for a class of memristive Cohen–Grossberg neural networks with time-varying delays by designing a...     

Global Exponential Stability and Existence of Periodic Solution of Impulsive Cohen–Grossberg Neural Networks with Distributed Delays on Time Scales

On time scales, by using the continuation theorem of coincidence degree theory, M-matrix theory and constructing some suitable Lyapunov functions, some sufficient conditions are obtained for the existence and exponential stability of periodic solutions of impulsive Cohen–Grossberg neural networks with distributed delays, which are new and complement of previously known results. Finally, an example is given to illustrate the effectiveness of our main results.     

Asymptotic Stability of Cohen–Grossberg BAM Neutral Type Neural Networks with Distributed Time Varying Delays

This paper is concerned with the problem of asymptotic stability of neutral type Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. By constructing a suitable Lyapunov–Krasovskii functional (LKF), reciprocal convex technique and Jensen’s inequality are used to delay-dependent conditions are established to analysis the asymptotic stability of Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. These stability conditions are formulated as linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms. Finally numerical examples are given to illustrate the usefulness of our proposed method.     

Asymptotic Stability and Polynomial Stability of Impulsive Cohen–Grossberg Neural Networks with Multi-proportional Delays

Neural Processing Letters - This paper is concerned with the global asymptotic stability (GAS) and global polynomial stability (GPS) of impulsive Cohen–Grossberg neural networks (ICGNNs) with...     

Stability and Bifurcation of a Class of Discrete-Time Cohen–Grossberg Neural Networks with Discrete Delays

A class of discrete-time Cohen–Grossberg neural networks with discrete delays and ring-architecture are investigated in this paper. By analyzing the corresponding characteristic equations, the existence of Neimark–Sacker bifurcations at the origin are obtained. By applying the normal form theory and the center manifold theorem, the direction of the Neimark–Sacker bifurcation and the stability of bifurcating periodic solutions are obtained. Sufficient conditions to guarantee the global stability of the null solution of such networks are established by using suitable Lyapunov function and the properties of M-matrix. Numerical simulations are given to illustrate the obtained results.     

Graph-Theoretic Approach to Finite-Time Synchronization for Fuzzy Cohen–Grossberg Neural Networks with Mixed Delays and Discontinuous Activations

Neural Processing Letters - Arguably the most recurring issue concerning network security is building an approach that is capable of detecting intrusions into network systems. This issue has been...     

Improved Stability Results for Stochastic Cohen–Grossberg Neural Networks with Discrete and Distributed Delays

This paper is concerned with the exponential stability problem for a class of stochastic Cohen–Grossberg neural networks with discrete and unbounded distributed time delays. By applying the Jensen integral inequality and the generalized Jensen integral inequality, several improved delay-dependent criteria are developed to achieve the exponential stability in mean square in terms of linear matrix inequalities. It is established theoretically that two special cases of the obtained criteria are less conservative than some existing results but including fewer slack variables. As the present conditions involve fewer free weighting matrices, the computational burden is largely reduced. Three numerical examples are provided to demonstrate the effectiveness of the theoretical results.     

Finite-Time Stability of Stochastic Cohen–Grossberg Neural Networks with Markovian Jumping Parameters and Distributed Time-Varying Delays

In this paper, the finite-time stability problem is considered for a class of stochastic Cohen–Grossberg neural networks (CGNNs) with Markovian jumping parameters and distributed time-varying delays. Based on Lyapunov–Krasovskii functional and stability analysis theory, a linear matrix inequality approach is developed to derive sufficient conditions for guaranteeing the stability of the concerned system. It is shown that the addressed stochastic CGNNs with Markovian jumping and distributed time varying delays are finite-time stable. An illustrative example is provided to show the effectiveness of the developed results.     

Discrete Analogue for a Class of Impulsive Cohen–Grossberg Neural Networks with Asynchronous Time-Varying Delays

Neural Processing Letters - This paper presents the exponential stability preservation in simulations of an impulsive Cohen–Grossberg neural networks with asynchronous time delays. By...     

Existence and Exponential Stability of Periodic Solution for BAM Fuzzy Cohen–Grossberg Neural Networks with Mixed Delays

In this paper, BAM fuzzy Cohen–Grossberg neural networks with mixed delays are considered. Using M-matrix theory and differential inequality techniques, some sufficient conditions for the existence and exponential stability of periodic solution to the neural networks are established. The results of this paper are completely new and complementary to the previously known results. Finally, an example is given to illustrate the effectiveness of our results obtained.     

Further Results on Input-to-State Stability of Stochastic Cohen–Grossberg BAM Neural Networks with Probabilistic Time-Varying Delays

Neural Processing Letters - In this article, the problem of stochastic Cohen–Grossberg Bidirectional Associative Memory (CGBAM) neural networks with probabilistic time-varying delay is...     

$$alpha $$ α -Exponential Stability of Impulsive Fractional-Order Complex-Valued Neural Networks with Time Delays

Neural Processing Letters - This paper investigates the global $$alpha $$ -exponential stability of impulsive fractional-order complex-valued neural networks with time delays. By constructing...     

Periodic Solution for Fuzzy Cohen–Grossberg BAM Neural Networks with Both Time-Varying and Distributed Delays and Variable Coefficients

In this paper, we investigate the existence and global exponential stability of periodic solution for a general class of fuzzy Cohen–Grossberg bidirectional associative memory (BAM) neural networks with both time-varying and (finite or infinite) distributed delays and variable coefficients. Some novel sufficient conditions for ascertaining the existence, uniqueness, global attractivity and exponential stability of the periodic solution to the considered system are obtained by applying matrix theory, inequality analysis technique and contraction mapping principle. The results remove the usual assumption that the activation functions are bounded and/or continuously differentiable. It is believed that these results are significant and useful for the design and applications of fuzzy Cohen–Grossberg BAM neural networks. Moreover, an example is employed to illustrate the effectiveness and feasibility of the results obtained here.     

Mittag–Leffler Stability and Global Asymptotically $$\omega $$-Periodicity of Fractional-Order BAM Neural Networks with Time-Varying Delays

This article studies the Mittag–Leffler stability and global asymptotical \(\omega \)-periodicity for a class of fractional-order bidirectional associative memory (BAM) neural networks with time-varying delays by using Laplace transform, stability theory of fractional systems and some integration technique. Firstly, some sufficient conditions are given to ensure the boundedness and global Mittaag-Leffler stability of fractional-order BAM neural networks with time-varying delays. Next, S-asymptotical \(\omega \)-periodicity and global asymptotical \(\omega \)-periodicity of fractional-order BAM neural networks with time-varying delays are also explored. Finally, some numerical examples and simulation are performed to show the effectiveness of theoretical results.     

Robust Stability in Cohen–Grossberg Neural Network with both Time-Varying and Distributed Delays

In this article, the global exponential robust stability is investigated for Cohen–Grossberg neural network with both time-varying and distributed delays. The parameter uncertainties are assumed to be time-invariant and bounded, and belong to given compact sets. Applying the idea of vector Lyapunov function, M-matrix theory and analysis techniques, several sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential robust stability of the equilibrium point for the neural network. The methodology developed in this article is shown to be simple and effective for the exponential robust stability analysis of neural networks with time-varying delays and distributed delays. The results obtained in this article extend and improve a few recently known results and remove some restrictions on the neural networks. Three examples are given to show the usefulness of the obtained results that are less restrictive than recently known criteria.      

Exponential p-Synchronization of Non-autonomous Cohen–Grossberg Neural Networks with Reaction-Diffusion Terms via Periodically Intermittent Control

The problem of \(p\) -synchronization for a class of stochastic non-autonomous reaction-diffusion Cohen–Grossberg networks with mixed delays by using periodically intermittent feedback control is investigated in this paper. Some exponential synchronization criteria based on \(p\) -norm are obtained by utilizing some analysis methods. These proofs indirectly generalized the Halanay inequality and facilitated the proof processing of the existing works. Finally, an illustrative example is given to show the effectiveness of the theoretical results.