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

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.

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Exponential synchronization of coupled memristive neural networks with time delays

Neural Computing and Applications ◽

10.1007/s00521-013-1349-3 ◽

2013 ◽

Vol 24 (6) ◽

pp. 1421-1430 ◽

Cited By ~ 52

Author(s):

Guan Wang ◽

Yi Shen

Keyword(s):

Neural Networks ◽

Time Delays ◽

Exponential Synchronization ◽

Memristive Neural Networks

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Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability

Mathematics ◽

10.3390/math8050815 ◽

2020 ◽

Vol 8 (5) ◽

pp. 815 ◽

Cited By ~ 4

Author(s):

Usa Humphries ◽

Grienggrai Rajchakit ◽

Pramet Kaewmesri ◽

Pharunyou Chanthorn ◽

Ramalingam Sriraman ◽

...

Keyword(s):

Neural Networks ◽

Continuous Time ◽

Lyapunov Functional ◽

Time Delays ◽

System Model ◽

Mean Square ◽

New Class ◽

Quaternion Multiplication ◽

The Mean ◽

Theoretical Results

In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying It o ^ ’s formula, Dynkin’s formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results.

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Exponential synchronization of memristive neural networks with time delays

Neurocomputing ◽

10.1016/j.neucom.2018.01.017 ◽

2018 ◽

Vol 297 ◽

pp. 1-7 ◽

Cited By ~ 3

Author(s):

Hongjuan Wu ◽

Yuming Feng ◽

Zhengwen Tu ◽

Jing Zhong ◽

Qingsong Zeng

Keyword(s):

Neural Networks ◽

Time Delays ◽

Exponential Synchronization ◽

Memristive Neural Networks

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Exponential Synchronization in Inertial Neural Networks with Time Delays

Electronics ◽

10.3390/electronics8030356 ◽

2019 ◽

Vol 8 (3) ◽

pp. 356 ◽

Cited By ~ 1

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.

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SYNCHRONIZATION IN LINEARLY COUPLED DYNAMICAL NETWORKS WITH DISTRIBUTED TIME DELAYS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127408021531 ◽

2008 ◽

Vol 18 (07) ◽

pp. 2039-2047 ◽

Cited By ~ 16

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.

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