Stochastic Synchronization of Impulsive Reaction–Diffusion BAM Neural Networks at a Fixed and Predetermined Time

Rouzimaimaiti Mahemuti (), Ehmet Kasim and Hayrengul Sadik
Additional contact information
Rouzimaimaiti Mahemuti: School of Information Technology and Engineering, Guangzhou College of Commerce, Guangzhou 511363, China
Ehmet Kasim: College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China
Hayrengul Sadik: College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China

Mathematics, 2024, vol. 12, issue 8, 1-19

Abstract: This paper discusses the synchronization problem of impulsive stochastic bidirectional associative memory neural networks with a diffusion term, specifically focusing on the fixed-time (FXT) and predefined-time (PDT) synchronization. First, a number of more relaxed lemmas are introduced for the FXT and PDT stability of general types of impulsive nonlinear systems. A controller that does not require a sign function is then proposed to ensure that the synchronization error converges to zero within a predetermined time. The controllerdesigned in this paper serves the additional purpose of preventing the use of an unreliable inequality in the course of proving the main results. Next, to guarantee FXT and PDT synchronization of the drive–response systems, this paper employs the Lyapunov function method and derives sufficient conditions. Finally, a numerical simulation is presented to validate the theoretical results.

Keywords: diffusion term; impulse effect; stochastic perturbations; predefined-time synchronization; fixed-time synchronization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/8/1204/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/8/1204/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:8:p:1204-:d:1377445

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().