Impulsive Fractional Cohen-Grossberg Neural Networks: Almost Periodicity Analysis

Date
2021-07-27
Authors
Stamova, Ivanka
Sotirov, Sotir
Sotirova, Evdokia
Stamov, Gani
Journal Title
Journal ISSN
Volume Title
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Abstract

In this paper, a fractional-order Cohen–Grossberg-type neural network with Caputo fractional derivatives is investigated. The notion of almost periodicity is adapted to the impulsive generalization of the model. General types of impulsive perturbations not necessarily at fixed moments are considered. Criteria for the existence and uniqueness of almost periodic waves are proposed. Furthermore, the global perfect Mittag–Leffler stability notion for the almost periodic solution is defined and studied. In addition, a robust global perfect Mittag–Leffler stability analysis is proposed. Lyapunov-type functions and fractional inequalities are applied in the proof. Since the type of Cohen–Grossberg neural networks generalizes several basic neural network models, this research contributes to the development of the investigations on numerous fractional neural network models.

Description
Keywords
fractional-order derivatives, impulses, Cohen–Grossberg neural networks, almost periodicity, perfect Mittag–Leffler stability, robustness
Citation
Fractal and Fractional 5 (3): 78 (2021)
Department
Mathematics