Design and Practical Stability of a New Class of Impulsive Fractional-Like Neural Networks

Gani Stamov; Ivanka Stamova; Anatoliy Martynyuk; Trayan Stamov

doi:10.3390/e22030337

Design and Practical Stability of a New Class of Impulsive Fractional-Like Neural Networks

Entropy (Basel). 2020 Mar 15;22(3):337. doi: 10.3390/e22030337.

Authors

Gani Stamov¹, Ivanka Stamova², Anatoliy Martynyuk³, Trayan Stamov⁴

Affiliations

¹ Department of Mathematics, Technical University of Sofia, 8800 Sliven, Bulgaria.
² Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA.
³ S.P. Timoshenko Institute of Mechanics, NAS of Ukraine, 03057 Kiev-57, Ukraine.
⁴ Department of Machine Elements and Non-metallic Constructions, Technical University of Sofia, Sofia 1000, Bulgaria.

Abstract

In this paper, a new class of impulsive neural networks with fractional-like derivatives is defined, and the practical stability properties of the solutions are investigated. The stability analysis exploits a new type of Lyapunov-like functions and their derivatives. Furthermore, the obtained results are applied to a bidirectional associative memory (BAM) neural network model with fractional-like derivatives. Some new results for the introduced neural network models with uncertain values of the parameters are also obtained.

Keywords: fractional-like derivative; h−manifolds; impulses; neural networks; practical stability.