scholarly journals Exponential Synchronization in Inertial Neural Networks with Time Delays

Electronics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 356 ◽  
Author(s):  
Liang Ke ◽  
Wanli Li
Keyword(s):  
Differential Equation ◽  
Neural Networks ◽  
Lyapunov Functional ◽  
Time Delays ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Inertial Neural Networks ◽  
Response Systems ◽  
Global Exponential Synchronization

In this paper, exponential synchronization for inertial neural networks with time delays is investigated. First, by introducing a directive Lyapunov functional, a sufficient condition is derived to ascertain the global exponential synchronization of the drive and response systems based on feedback control. Second, by introducing a variable substitution, the second-order differential equation is transformed into a first-order differential equation. As such, a new Lyapunov functional is constructed to formulate a novel global exponential synchronization for the systems under study. The two obtained sufficient conditions complement each other and are suitable to be applied in different cases. Finally, two numerical examples are given to illustrated the effectiveness of the proposed theoretical results.

Stabilization for a class of delayed switched inertial neural networks via non-reduced order method

2021 ◽  
pp. 014233122098594
Author(s):  
Xuan Chen ◽  
Dongyun Lin
Keyword(s):  
Neural Networks ◽  
Comparative Research ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Global Stabilization ◽  
Order Method ◽  
Reduced Order ◽  
Global Asymptotic Stabilization ◽  
Inertial Neural Networks ◽  
Barbalat Lemma

This paper tackles the issue of global stabilization for a class of delayed switched inertial neural networks (SINN). Distinct from the frequently employed reduced-order technique, this paper studies SINN directly through non-reduced order method. By constructing a novel Lyapunov functional and using Barbalat Lemma, sufficient conditions for the global asymptotic stabilization issue and global exponential stabilization issue of the considered SINN are established. Numerical simulations further confirm the feasibility of the main results. The comparative research shows that global stabilization results of this paper complement and improve some existing work.

scholarly journals Exponential Synchronization for Stochastic Neural Networks with Mixed Time Delays and Markovian Jump Parameters via Sampled Data

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Yingwei Li ◽  
Xueqing Guo
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Stochastic Neural Networks ◽  
Sampled Data ◽  
Markovian Jump ◽  
Markovian Jump Parameters ◽  
Mixed Time Delays ◽  
Data Controller

The exponential synchronization issue for stochastic neural networks (SNNs) with mixed time delays and Markovian jump parameters using sampled-data controller is investigated. Based on a novel Lyapunov-Krasovskii functional, stochastic analysis theory, and linear matrix inequality (LMI) approach, we derived some novel sufficient conditions that guarantee that the master systems exponentially synchronize with the slave systems. The design method of the desired sampled-data controller is also proposed. To reflect the most dynamical behaviors of the system, both Markovian jump parameters and stochastic disturbance are considered, where stochastic disturbances are given in the form of a Brownian motion. The results obtained in this paper are a little conservative comparing the previous results in the literature. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

scholarly journals Periodic solution for inertial neural networks with variable parameters

2021 ◽  
Vol 6 (12) ◽  
pp. 13580-13591
Author(s):  
Lingping Zhang ◽  
◽  
Bo Du
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Asymptotic Stability ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Mawhin’S Continuation Theorem ◽  
Variable Parameters ◽  
Inertial Neural Networks ◽  
Lyapunov Functional Method

<abstract><p>We discuss periodic solution problems and asymptotic stability for inertial neural networks with $ D- $operator and variable parameters. Based on Mawhin's continuation theorem and Lyapunov functional method, some new sufficient conditions on the existence and asymptotic stability of periodic solutions are established. Finally, a numerical example verifies the effectiveness of the obtained results.</p></abstract>

SYNCHRONIZATION IN LINEARLY COUPLED DYNAMICAL NETWORKS WITH DISTRIBUTED TIME DELAYS

2008 ◽  
Vol 18 (07) ◽  
pp. 2039-2047 ◽  
Author(s):  
CHUN-HSIEN LI ◽  
SUH-YUH YANG
Keyword(s):  
Lyapunov Functional ◽  
Time Delays ◽  
Exponential Synchronization ◽  
Matrix Inequality ◽  
Dynamical Networks ◽  
Distributed Time Delays ◽  
Inequality Techniques ◽  
Simulation Results ◽  
Global Exponential Synchronization ◽  
Theoretical Analyses

In this paper, we investigate the global exponential synchronization of linearly coupled dynamical networks with time delays. The time delay considered is of the distributed type and the outer-coupling matrix is not assumed to be symmetric. Employing the Lyapunov functional and matrix inequality techniques, we propose a sufficient condition for the occurrence of global exponential synchronization. Two illustrative examples, the coupled Chua's circuits and the coupled Hindmarsh–Rose neurons, and their numerical simulation results are presented to demonstrate the theoretical analyses.

scholarly journals Global exponential synchronization of quaternion-valued memristive neural networks with time delays

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Ruoyu Wei ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Differential Inclusion ◽  
Lyapunov Functional ◽  
Time Delays ◽  
Exponential Synchronization ◽  
The Other ◽  
Memristive Neural Networks ◽  
Global Synchronization ◽  
New Class ◽  
Inequality Techniques

This paper extends the memristive neural networks (MNNs) to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established, and the problem of drive-response global synchronization of this type of networks is investigated in this paper. Two cases are taken into consideration: one is with the conventional differential inclusion assumption, the other without. Criteria for the global synchronization of these two cases are achieved respectively by appropriately choosing the Lyapunov functional and applying some inequality techniques. Finally, corresponding simulation examples are presented to demonstrate the correctness of the proposed results derived in this paper.

EXPONENTIAL SYNCHRONIZATION IN DRIVE-RESPONSE SYSTEMS OF HOPFIELD-TYPE NEURAL NETWORKS WITH TIME DELAYS

2007 ◽  
Vol 17 (11) ◽  
pp. 4167-4176 ◽  
Author(s):  
CHUN-HSIEN LI ◽  
SUH-YUH YANG
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Functional Method ◽  
Exponential Synchronization ◽  
Weighted Sum ◽  
Response Type ◽  
Response Systems ◽  
Coupling Strengths ◽  
Lyapunov Functional Method ◽  
Exponential Rates

In this paper we investigate the drive-response type synchronization of Hopfield-type neural networks with connection time delays for both discrete and distributed cases. By employing the Lyapunov functional method, we propose a sufficient condition to ensure the occurrence of synchronization with exponential rates. This criterion is independent of time delays as well as the types of delay. We prove that the exponential synchronization occurs provided a certain weighted sum of the connection and coupling strengths is negative enough, no matter that the connection time delay is of discrete or distributed case. Numerical examples are provided to illustrate the results.

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