Existence and global asymptotic stability of positive periodic solution of delayed Cohen–Grossberg neural networks

Hien, Le Van; Loan, Tran Thi; Trang, B. T. Huyen; Trinh, Hieu

doi:10.1016/j.amc.2014.04.078

Cited by 22 publications

(9 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It follows that y D .y 1 , : : : , y n / T maps D OE k 1 , k 1 OE k 2 , k 2 OE k n , k n into itself. Therefore, by Brower's fixed point theorem, y has at least one equilibrium point for system (1). This completes the proof.…”

Section: Proofsupporting

confidence: 57%

“…The activation function g j .x j .t// denotes the output of the j th neuron at time t. y i .t/ is the output, and a ij , b ij and c ij are the connection weights of the neural networks, respectively. In the neural network (1), the bounded functions .t/ and ı.t/ represent the discrete and distributed time-varying delays with 0 Ä .t/ Ä , P .t/ Ä and 0 Ä ı.t/ Ä ı.…”

Section: Notations and Preliminary Resultsmentioning

confidence: 99%

“…Besides, in order to obtain less conservative stability criteria, numerous important and interesting methods have been proposed, for example, free‐weighting matrix technique, Wirtinger‐based integral inequality, a convex optimization approach, delay‐fraction technique, and constructing new Lyapunov–Krasovskii functional (LKF) containing triple‐integral terms. However, based on the applications of CGNNs, the authors in discussed the problem of existence and global asymptotic stability of positive periodic solution of delayed CGNNs. In , the author studied stability analysis of reaction–diffusion CGNNs under impulsive control.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A quadratic convex combination approach on robust dissipativity and passivity analysis for Takagi–Sugeno fuzzy Cohen–Grossberg neural networks with time‐varying delays

Nagamani

Radhika

2016

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, the robust dissipativity and passivity criteria for Takagi-Sugeno fuzzy Cohen-Grossberg neural networks with time-varying delays have been investigated. The delay is of the time-varying nature, and the activation functions are assumed to be neither differentiable nor strictly monotonic. Furthermore, the description of the activation functions is more general than the commonly used Lipschitz conditions. By using a Lyapunov-Krasovskii functional and employing the quadratic convex combination approach, a set of sufficient conditions are established to ensure the dissipativity of the proposed model. The obtained conditions are presented in terms of linear matrix inequalities, so that its feasibility can be checked easily via standard numerical toolboxes. The quadratic convex combination approach used in our paper gives a reduced conservatism without using Jensen's inequality. In addition to that, numerical examples with simulation results are given to show the effectiveness of the obtained linear matrix inequality conditions.

show abstract

Section: Proofsupporting

confidence: 57%

Section: Notations and Preliminary Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A quadratic convex combination approach on robust dissipativity and passivity analysis for Takagi–Sugeno fuzzy Cohen–Grossberg neural networks with time‐varying delays

Nagamani

Radhika

2016

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…}, the fixed impulsive moments t k satisfy t k−1 < t k and lim k→+∞ t k = +∞, δ(t) is the Dirac impulsive function, which means that the state of network (1) has jumps at t k for k ∈ N. u jk and w jk represent the strength of impulsive effects of the jth neuron at time t k and t k − τ (t), respectively. If u jk = w jk = 0, then model (1) becomes continuous neural network models (see [2,18,19]). …”

Section: Preliminariesmentioning

confidence: 99%

“…Meanwhile, network (16) is globally uniformly exponentially convergent to the ball (19). λ > 0 is a unique solution of the equality λ = a − be λτ and λ m = min 1≤i≤n {p i }.…”

Section: Theoremmentioning

confidence: 99%

Exponential convergence and Lagrange stability for impulsive Cohen–Grossberg neural networks with time-varying delays

Jian

2015

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

h i g h l i g h t s• We discuss Lagrange stability for impulsive Cohen-Grossberg neural networks.• We establish a new delay impulsive differential inequality. • Some easily verified conditions of Lagrange exponential stability are obtained.• Giving out the detail estimations of the exponential convergence ball.• The results here generalize and improve the earlier publications. a b s t r a c tIn this paper, the problem on exponential convergence and Lagrange exponential stability for a class of delayed Cohen-Grossberg neural networks with impulses effects is investigated. To this end, a new delay impulsive differential inequality is established, which improves and generalizes previously known criteria. By using the new inequality and coupling with the Lyapunov method, several sufficient conditions are derived to guarantee the global exponential stability in Lagrange sense and exponential convergence of the state variables of the discussed delayed Cohen-Grossberg neural networks with impulses effects. Meanwhile, the framework of the exponential convergence ball in the state space with a pre-specified convergence rate is also given. Here, the existence and uniqueness of the equilibrium points need not to be considered. Finally, some numerical examples with simulation show the effectiveness of the obtained results.

show abstract

Exponential stability of positive neural networks in bidirectional associative memory model with delays

Hien

Hai-An

2019

Math Methods in App Sciences

View full text Add to dashboard Cite

This paper is concerned with the problem of exponential stability of positive neural networks in bidirectional associative memory (BAM) model with multiple time-varying delays and nonlinear self-excitation rates. On the basis of a systematic approach involving extended comparison techniques via differential inequalities, we first prove the positivity of state trajectories initializing from a positive cone called the admissible set of initial conditions. In combination with the use of Brouwer's fixed point theorem and M-matrix theory, we then derive conditions for the existence and global exponential stability of a unique positive equilibrium of the model. An extension to the case of BAM neural networks with proportional delays is also presented. The effectiveness of the obtained results is illustrated by a numerical example with simulations. KEYWORDS exponential stability, M-matrix, positve BAM neural networks, time-varying delays MSC CLASSIFICATION 34 K20; 34 K45; 92C42

show abstract

Existence and global asymptotic stability of positive periodic solution of delayed Cohen–Grossberg neural networks

Cited by 22 publications

References 39 publications

A quadratic convex combination approach on robust dissipativity and passivity analysis for Takagi–Sugeno fuzzy Cohen–Grossberg neural networks with time‐varying delays

A quadratic convex combination approach on robust dissipativity and passivity analysis for Takagi–Sugeno fuzzy Cohen–Grossberg neural networks with time‐varying delays

Exponential convergence and Lagrange stability for impulsive Cohen–Grossberg neural networks with time-varying delays

Exponential stability of positive neural networks in bidirectional associative memory model with delays

Contact Info

Product

Resources

About