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...     

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.     

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...     

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.     

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...     

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.     

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.     

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.      

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.     

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.     

The Boundedness and the Global Mittag-Leffler Synchronization of Fractional-Order Inertial Cohen–Grossberg Neural Networks with Time Delays

Neural Processing Letters - The boundedness and the global Mittag-Leffler synchronization (GMLS) of fractional-order inertial Cohen–Grossberg neural networks (CGNNS) with time delays are...     

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...     

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...     

$$alpha $$ 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...     

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...     

Existence and Exponential Stability of Anti-periodic Solutions for a High-Order Delayed Cohen–Grossberg Neural Networks with Impulsive Effects

In this paper, a high-order Cohen–Grossberg neural networks with bounded, unbounded delays and impulses is considered. By using differential inequality techniques, some very verifiable criteria on the existence and exponential stability of anti-periodic solutions for the model are obtained. Our results are new and complementary to previously known results. An example is included to illustrate the feasibility and effectiveness of our main results.     

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.     

$${\varvec{}}$$th Moment Exonential Stability of Hybrid Delayed Reaction–Diffusion Cohen–Grossberg Neural Networks

In this paper, we propose hybrid reaction–diffusion Cohen–Grossberg neural networks (RDCGNNs) with variable coefficients and mixed time delays. By using the Lyapunov–Krasovkii functional approach, stochastic analysis technique and Hardy inequality, some novel sufficient conditions are derived to ensure the pth moment exponential stability of hybrid RDCGNNs with mixed time delays. The obtained sufficient conditions are relevant to the diffusion terms. The results of this paper are novel and improve some of the previously known results. Finally, two numerical examples are provided to verify the usefulness of the obtained results.