Generalized non-autonomous Cohen-Grossberg neural network model

In the present paper, we investigate both the global exponential stability and the existence of a periodic solution of a general differential equation with unbounded distributed delays. The main stability criterion depends on the dominance of the non-delay terms over the delay terms. The criterion for the existence of a periodic solution is obtained with the application of the coincide degree theorem. We use the main results to get criteria for the existence and global exponential stability of periodic solutions of a generalized higher-order periodic Cohen-Grossberg neural network model with discrete-time varying delays and infinite distributed delays. Additionally, we provide a comparison with the results in the literature and a numerical simulation to illustrate the effectiveness of some of our results.Comment: 30 page

Cohen-Grossberg neural networks with unpredictable and Poisson stable dynamics

In this paper, Cohen-Grossberg neural networks with unpredictable and compartmental periodic unpredictable strengths of connectivity between cells and inputs are investigated. To approve Poisson stability and unpredictability in neural networks, the method of included intervals and contraction mapping principle are used. The existence, uniqueness, and exponential stability of unpredictable and Poisson stable outputs are discussed. Examples with numerical simulations that support the theoretical results are provided. The dependence of the neural network dynamics on the numerical characteristic, the degree of periodicity, is shown

Existence and Global Uniform Asymptotic Stability of Pseudo Almost Periodic Solutions for Cohen-Grossberg Neural Networks with Discrete and Distributed Delays

This paper studies the existence and uniform asymptotic stability of pseudo almost periodic solutions to Cohen-Grossberg neural networks (CGNNs) with discrete and distributed delays by applying Schauder fixed point theorem and constructing a suitable Lyapunov functional. An example is given to show the effectiveness of the main results

Fixed-time control of delayed neural networks with impulsive perturbations

This paper is concerned with the fixed-time stability of delayed neural networks with impulsive perturbations. By means of inequality analysis technique and Lyapunov function method, some novel fixed-time stability criteria for the addressed neural networks are derived in terms of linear matrix inequalities (LMIs). The settling time can be estimated without depending on any initial conditions but only on the designed controllers. In addition, two different controllers are designed for the impulsive delayed neural networks. Moreover, each controller involves three parts, in which each part has different role in the stabilization of the addressed neural networks. Finally, two numerical examples are provided to illustrate the effectiveness of the theoretical analysis

Almost Periodic Dynamics for Memristor-Based Shunting Inhibitory Cellular Neural Networks with Leakage Delays

We investigate a class of memristor-based shunting inhibitory cellular neural networks with leakage delays. By applying a new Lyapunov function method, we prove that the neural network which has a unique almost periodic solution is globally exponentially stable. Moreover, the theoretical findings of this paper on the almost periodic solution are applied to prove the existence and stability of periodic solution for memristor-based shunting inhibitory cellular neural networks with leakage delays and periodic coefficients. An example is given to illustrate the effectiveness of the theoretical results. The results obtained in this paper are completely new and complement the previously known studies of Wu (2011) and Chen and Cao (2002)

Exponential Lag Synchronization of Cohen-Grossberg Neural Networks with Discrete and Distributed Delays on Time Scales

In this article, we investigate exponential lag synchronization results for the Cohen-Grossberg neural networks (C-GNNs) with discrete and distributed delays on an arbitrary time domain by applying feedback control. We formulate the problem by using the time scales theory so that the results can be applied to any uniform or non-uniform time domains. Also, we provide a comparison of results that shows that obtained results are unified and generalize the existing results. Mainly, we use the unified matrix-measure theory and Halanay inequality to establish these results. In the last section, we provide two simulated examples for different time domains to show the effectiveness and generality of the obtained analytical results.Comment: 20 pages, 18 figure

Quasi-synchronization of delayed coupled networks with non-identical discontinuous nodes

This paper is concerned with the quasi-synchronization issue of linearly coupled networks with discontinuous nonlinear functions in each isolated node. Under the framework of Filippov systems, the existence and boundedness of solutions for such complex networks can be guaranteed by the matrix measure approach. A design method is presented for the synchronization controllers of coupled networks with non-identical discontinuous systems. Numerical simulations on the coupled chaotic systems are given to demonstrate the effectiveness of the theoretical results

Further analysis of stability of uncertain neural networks with multiple time delays

This paper studies the robust stability of uncertain neural networks with multiple time delays with respect to the class of nondecreasing activation functions. By using the Lyapunov functional and homeomorphism mapping theorems, we derive a new delay-independent sufficient condition the existence, uniqueness, and global asymptotic stability of the equilibrium point for delayed neural networks with uncertain network parameters. The condition obtained for the robust stability establishes a matrix-norm relationship between the network parameters of the neural system, and therefore it can easily be verified. We also present some constructive numerical examples to compare the proposed result with results in the previously published corresponding literature. These comparative examples show that our new condition can be considered as an alternative result to the previous corresponding literature results as it defines a new set of network parameters ensuring the robust stability of delayed neural networks.Publisher's Versio