# Information Processing with Stability Point Modeling in Cohen–Grossberg Neural Networks

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Cohen–Grossberg Network Training for Different Modalities

## 3. H-Stability Results

**Theorem**

**1.**

- There exists a positive number (μ), and$$\begin{array}{cc}\hfill \phantom{\rule{1.em}{0ex}}& mi{n}_{1\le i\le n}\left(\underline{{a}_{i}}{B}_{i}-\overline{{a}_{j}}\sum _{j=1}^{m}|{p}_{ij}\left|{\widehat{L}}_{i}\right|\right)+mi{n}_{1\le j\le m}\left(\underline{\widehat{{a}_{j}}}\widehat{{B}_{j}}-{\widehat{\overline{a}}}_{j}\sum _{i=1}^{n}|{c}_{ij}\left|{L}_{j}\right|\right)\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& -\left(ma{x}_{1\le j\le m}\overline{{a}_{j}}\sum _{i=1}^{n}|{d}_{ij}|{M}_{j}+ma{x}_{1\le i\le n}\widehat{\overline{{a}_{i}}}\sum _{j=1}^{m}\left|{q}_{ij}\right|{\widehat{M}}_{i}\right)\ge \mu ;\hfill \end{array}$$
- The functions ${P}_{ik}$ and ${Q}_{jk}$ are such that$${P}_{ik}\left({x}_{i}\left({t}_{k}\right)\right)=-{\gamma}_{ik}({x}_{i}\left({t}_{k}\right)-{x}_{i}^{*}),{Q}_{jk}\left({y}_{j}\left({t}_{k}\right)\right)=-{\mu}_{jk}({y}_{j}\left({t}_{k}\right)-{y}_{j}^{*}),$$
- Such a function exists ($h(t,z)$), where the following inequalities hold [19,20,21]:$$\parallel h(t,z)\parallel \le \parallel z\parallel <\Lambda \left(H\right)\parallel h(t,z)\parallel ,(t,z)\in \left[{t}_{0},\infty \right)\times {\mathbb{R}}^{n+m},$$

## 4. Algorithms of a Stability Model in Cohen–Grossberg-Type Neural Networks

`C`programming language. We used

`OpenMPI`technology [26] on a cluster of eight machines, each equipped with four Intel

^{®}Xeon

^{®}[27] processors.

## 5. Implementation

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ANN | Artificial neural network |

CGNN | Cohen–Grossberg neural network |

IS | Intelligent system |

LTM | Long-term memory |

STM | Short-term memory |

OpenMPI | Open message-passing interface |

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**MDPI and ACS Style**

Gospodinova, E.; Torlakov, I.
Information Processing with Stability Point Modeling in Cohen–Grossberg Neural Networks. *Axioms* **2023**, *12*, 612.
https://doi.org/10.3390/axioms12070612

**AMA Style**

Gospodinova E, Torlakov I.
Information Processing with Stability Point Modeling in Cohen–Grossberg Neural Networks. *Axioms*. 2023; 12(7):612.
https://doi.org/10.3390/axioms12070612

**Chicago/Turabian Style**

Gospodinova, Ekaterina, and Ivan Torlakov.
2023. "Information Processing with Stability Point Modeling in Cohen–Grossberg Neural Networks" *Axioms* 12, no. 7: 612.
https://doi.org/10.3390/axioms12070612