Cohen Grossberg-type Bidirectional Associative Memory Research Articles

On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays

The present paper is devoted to Bidirectional Associative Memory (BAM) Cohen–Grossberg-type impulsive neural networks with time-varying delays. Instead of impulsive discontinuities at fixed moments of time, we consider variable impulsive perturbations. The stability with respect to manifolds notion is introduced for the neural network model under consideration. By means of the Lyapunov function method sufficient conditions that guarantee the stability properties of solutions are established. Two examples are presented to show the validity of the proposed stability criteria.

Robust stability of uncertain Markovian jumping stochastic Cohen-Grossberg type bam neural networks with time-varying delays and reaction diffusion terms

In this paper, the robust exponential stability problem is investigated for a class of uncertain Markovian jumping stochastic Cohen-Grossberg type bidirectional associative memory neural networks (...

Existence and exponential stability of periodic solution for a class of Cohen–Grossberg-type BAM neural networks

In this paper, we present a general class of hybrid bi-directional associative memory (BAM) neural networks. By using M-matrix theory, inequality technique and other analysis techniques, we investigate the exponential stability and the existence of periodic solutions for this kind of neural networks and sufficient conditions are obtained. The results generalize and improve some previous known results. Finally, two examples are given to demonstrate the effectiveness of the results obtained.

Formula omitted] almost periodic attractors for Cohen–Grossberg-type BAM neural networks with variable coefficients and distributed delays

In this paper, a class of 2 N almost periodic attractors for Cohen–Grossberg-type bi-directional associative memory (BAM) neural networks with variable coefficients and distributed delays is discussed. By imposing some new assumptions on activation functions and system parameters, we split invariant basin of BAM into 2 N compact convex subsets. Then the existence of 2 N almost periodic solutions lying in compact convex subsets is attained. And some new criteria for the networks to converge toward these 2 N almost periodic solutions and exponential attracting domains are also given correspondingly. Finally, some examples are presented to illustrate the feasibility and effectiveness of the results.

Impulsive effect on the delayed Cohen–Grossberg-type BAM neural networks

In the present paper, an impulsive Cohen–Grossberg-type bi-directional associative memory (BAM) neural network with distributed delays is studied. A set of new sufficient conditions are established for the existence and global exponential stability of a unique equilibrium without strict conditions imposed on self-regulation functions. Applying the results to some special cases, the obtained results generalize some previously known results. A variety of methods are employed to investigate the issue. The approaches are based on Banach fixed point theory, Brower fixed point theory, Laypunov–Kravsovskii functional, homeomorphism theory and the matrix spectral theory. It is believed that these results are helpful for the design and applications of the impulsive Cohen–Grossberg BAM type artificial neural networks.

Bi-periodicity evoked by periodic external inputs in delayed Cohen–Grossberg-type bidirectional associative memory networks

In this paper, the bi-periodicity issue is discussed for Cohen–Grossberg–type (CG-type) bidirectional associative memory (BAM) neural networks (NNs) with time-varying delays and standard activation functions. It is shown that the model considered in this paper has two periodic orbits located in saturation regions and they are locally exponentially stable. Meanwhile, some conditions are derived to ensure that, in any designated region, the model has a locally exponentially stable or globally exponentially attractive periodic orbit located in it. As a special case of bi-periodicity, some results are also presented for the system with constant external inputs. Finally, four examples are given to illustrate the effectiveness of the obtained results.

Stability in impulsive Cohen–Grossberg-type BAM neural networks with distributed delays

In this paper, a class of impulsive Cohen–Grossberg-type bi-directional associative memory (BAM) neural networks with distributed delays is investigated. By establishing an integro-differential inequality with impulsive initial conditions and employing the homeomorphism theory, the M-matrix theory and inequality technique, some new general sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive Cohen–Grossberg-type BAM neural networks with distributed delays are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on the system parameters and impulsive disturbed intension. An example is given to show the effectiveness of the results obtained here.

Almost periodic solution to Cohen–Grossberg-type BAM networks with distributed delays

In this paper, a class of Cohen–Grossberg-type bi-directional associative memory (BAM) neural networks with distributed delays is discussed. Based on inequality analysis method and combining the exponential dichotomy with fixed point theorem, some novel sufficient conditions are obtained to ensure the existence and globally exponential stability of almost periodic solution to this system. Moreover, an example is given to demonstrate the feasibility of our results.

Robust stability of uncertain fuzzy Cohen–Grossberg BAM neural networks with time-varying delays

In this paper, the Takagi–Sugeno (TS) fuzzy model representation is extended to the stability analysis for uncertain Cohen–Grossberg type bidirectional associative memory (BAM) neural networks with time-varying delays using linear matrix inequality (LMI) theory. A novel LMI-based stability criterion is obtained by using LMI optimization algorithms to guarantee the asymptotic stability of uncertain Cohen–Grossberg BAM neural networks with time varying delays which are represented by TS fuzzy models. Finally, the proposed stability conditions are demonstrated with numerical examples.

Exponential stability of periodic solution to Cohen–Grossberg-type BAM networks with time-varying delays

Periodic solutions can represent various storage patterns or memory patterns in some applications. In this paper, the existence and global exponential stability of periodic solution are discussed for the Cohen–Grossberg-type bidirectional associative memory (BAM) neural networks with time-varying delays. By applying the analysis method and inequality technique, some novel sufficient conditions are obtained to ensure the existence, uniqueness, global attractivity and exponential stability of the periodic solution to the considered system. Moreover, two examples are also given to demonstrate the feasibility of the obtained results.

Impulsive effects on stability of Cohen–Grossberg-type bidirectional associative memory neural networks with delays

In this paper, the exponential stability is investigated for a class of Cohen–Grossberg-type bidirectional associative memory neural networks with delays and impulsive effects. By using Lyapunov functionals, the analysis method, inequality technique and the properties of an M -matrix, the delay-independent sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point are derived. The obtained results are less restrictive than those given in the earlier literature, and the boundedness and differentiability of the activation functions are removed. An illustrative example is given to demonstrate the effectiveness of the obtained results.

Linear matrix inequality-based criteria for exponential robust stability of Cohen–Grossberg-type bidirectional associative memory neural networks with delays

The issue of global exponential robust stability is discussed for Cohen–Grossberg-type (CG-type) bidirectional associative memory (BAM) neural networks with delays. The activation functions that are adopted contain sigmoid functions and Lipschitz functions. For CG-type BAM neural networks with parameter uncertainties, which are assumed to be time invariant and bounded, by employing a Lyapunov–Krasovskii functional and linear matrix inequality (LMI) approach, the conditions ensuring global exponential robust stability are derived, which are expressed in terms of LMIs, and can be checked easily using the MATLAB LMI toolbox. In addition, when parameter uncertainties vanish, global exponential stability as a byproduct of global exponential robust stability, can also be guaranteed. Finally, two examples are provided to illustrate the effectiveness of the obtained results.

Exponential p-stability of delayed Cohen–Grossberg-type BAM neural networks with impulses

An impulsive Cohen–Grossberg-type bidirectional associative memory (BAM) neural networks with distributed delays is studied. Some new sufficient conditions are established for the existence and global exponential stability of a unique equilibrium without strict conditions imposed on self regulation functions. The approaches are based on Laypunov–Kravsovskii functional and homeomorphism theory. When our results are applied to the BAM neural networks, our results generalize some previously known results. It is believed that these results are significant and useful for the design and applications of Cohen–Grossberg-type bidirectional associative memory networks.

Stability in Cohen–Grossberg-type bidirectional associative memory neural networks with time-varying delays

In this paper, the exponential stability problem is investigated for a class of Cohen–Grossberg-type bidirectional associative memory neural networks with time-varying delays. By using the analysis method, inequality technique and the properties of an M-matrix, several novel sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point are derived. Moreover, the exponential convergence rate is estimated. The obtained results are less restrictive than those given in the earlier literature, and the boundedness and differentiability of the activation functions and differentiability of the time-varying delays are removed. Two examples with their simulations are given to show the effectiveness of the obtained results.