## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2013, Special Issue (2013), Article ID 196139, 13 pages.

### Existence and Global Exponential Stability of Equilibrium for Impulsive Cellular Neural Network Models with Piecewise Alternately Advanced and Retarded Argument

**Full-text: Open access**

#### Abstract

We introduce impulsive cellular neural network models with piecewise alternately advanced and retarded argument (in short IDEPCA). The model with the advanced argument is system with strong anticipation. Some sufficient conditions are established for the existence and global exponential stability of a unique equilibrium. The approaches are based on employing Banach’s fixed point theorem and a new IDEPCA integral inequality of Gronwall type. The criteria given are easily verifiable, possess many adjustable parameters, and depend on impulses and piecewise constant argument deviations, which provides exibility for the design and analysis of cellular neural network models. Several numerical examples and simulations are also given to show the feasibility and effectiveness of our results.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 196139, 13 pages.

**Dates**

First available in Project Euclid: 26 February 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1393449711

**Digital Object Identifier**

doi:10.1155/2013/196139

**Mathematical Reviews number (MathSciNet)**

MR3147863

**Zentralblatt MATH identifier**

1298.34136

#### Citation

Chiu, Kuo-Shou. Existence and Global Exponential Stability of Equilibrium for Impulsive Cellular Neural Network Models with Piecewise Alternately Advanced and Retarded Argument. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 196139, 13 pages. doi:10.1155/2013/196139. https://projecteuclid.org/euclid.aaa/1393449711

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