Fixed-time synchronization of competitive neural networks with proportional delays and impulsive effect
- PDF / 551,221 Bytes
- 10 Pages / 595.276 x 790.866 pts Page_size
- 82 Downloads / 220 Views
(0123456789().,-volV)(0123456789(). ,- volV)
ORIGINAL ARTICLE
Fixed-time synchronization of competitive neural networks with proportional delays and impulsive effect Chaouki Aouiti1
•
El Abed Assali1 • Farouk Che´rif2,3 • Anis Zeglaoui3,4
Received: 21 September 2018 / Accepted: 3 December 2019 Springer-Verlag London Ltd., part of Springer Nature 2019
Abstract This paper investigates the fixed-time synchronization problems for competitive neural networks with proportional delays and impulsive effect. The concerned network involves two coupling terms, i.e., long-term memory and short-term memory, which leads to the difficulty to the dynamics analysis. Based on Lyapunov functionals, the differential inequalities and for the objective of making the settling time independent of initial condition, a novel criterion guaranteeing the fixed-time synchronization of addressed system is derived. Finally, two examples and their simulations are given to demonstrate the effectiveness of the obtained results. Keywords Competitive neural networks Fixed-time synchronization Proportional delays Impulse Mathematics Subject Classification 34C27 37B25 92C20
1 Introduction In recent years, various neural networks (NNs) such as cellular neural networks, Hopfield neural networks, bidirectional associative memory neural networks, and competitive neural networks have been extensively studied in both theory and application, and they have been successfully applied to signal processing, pattern recognition, & Chaouki Aouiti [email protected]; [email protected] El Abed Assali [email protected] Farouk Che´rif [email protected] Anis Zeglaoui [email protected] 1
Faculty of Sciences of Bizerta, Department of Mathematics, Research Units of Mathematics and Applications UR13ES47, University of Carthage, BP, 7021 Zarzouna, Bizerta, Tunisia
2
Department of Mathematics, College of Science, King Khalid University, Abha 9004, Saudi Arabia
3
MaPSFA-ESST Hammam Sousse, ISSAT, University of Sousse, Sousse, Tunisia
4
LAMMDA-ESST Hammam Sousse, University of Sousse, Sousse, Tunisia
associative memory, optimization problems, [1–4] and multiscale modeling [5–8]. For example, the authors in [5] present an artificial NNs-based multiscale method for coupling continuum and molecular simulations. In [6], the authors investigated the development of a neural network approach in conjunction with molecular dynamics simulations. One of the popular NNs is competitive neural networks (CompNNs) which is introduced by Cohen and Grossberg [9] in 1983. Recently, Meyer-Ba¨se [10] proposed in 1996 the so-called CompNNs with different time scales. So, CompNNs with different time scales are extensions of Hopfield neural networks [11, 12], Grossberg’s shunting network [13] and Amaris model for primitive neuronal competition [14], which model the dynamics of cortical cognitive maps with unsupervised synaptic modifications. In the model of CompNNs, there are two types of state variable: that of the (STM: short-term memory) describ
Data Loading...
