scholarly journals Synchronization Analysis of a Class of Neural Networks with Multiple Time Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Changyou Wang ◽  
Qiang Yang ◽  
Tao Jiang ◽  
Nan Li
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Lyapunov Function ◽  
Differential Inequality ◽  
Time Delays ◽  
Multiple Delays ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
Delay Differential ◽  
Delay Differential Inequality

In this paper, we study the synchronization of a new fractional-order neural network with multiple delays. Based on the control theory of linear systems with multiple delays, we get the controller to analyse the synchronization of the system. In addition, a suitable Lyapunov function is constructed by using the theory of delay differential inequality, and some criteria ensuring the synchronization of delay fractional neural networks with Caputo derivatives are obtained. Finally, the accuracy of the method is verified by a numerical example.

Hopf Bifurcation of a Type of Neuron Model with Multiple Time Delays

2019 ◽  
Vol 29 (12) ◽  
pp. 1950163 ◽  
Author(s):  
Suqi Ma
Keyword(s):  
Hopf Bifurcation ◽  
Parameter Space ◽  
Time Delays ◽  
Neuron Model ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
The Stability ◽  
Geometrical Scheme ◽  
Delay Differential ◽  
Two Parameter

By applying a geometrical scheme developed to tackle the eigenvalue problem of delay differential equations with multiple time delays, Hopf bifurcation of Hopfield neuron model is analyzed in two-parameter space. By the introduction of two new angles, the calculation of imaginary roots is carried out analytically and effectively. By increasing the parameter to cross over the Hopf bifurcation lines, the stability switching direction is confirmed. The method is a useful tool to show the partition of stable and unstable regions in two-parameter space and detect double Hopf bifurcation further. The typified dynamical behaviors based on nearby double Hopf points are analyzed by applying the normal form technique and center manifold method.

scholarly journals Attracting and Quasi-Invariant Sets of Cohen-Grossberg Neural Networks with Time Delay in the Leakage Term under Impulsive Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Guiying Chen ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Differential Inequality ◽  
Invariant Sets ◽  
Leakage Term ◽  
Impulsive Perturbations ◽  
Delay Differential ◽  
Delay Differential Inequality

A class of impulsive Cohen-Grossberg neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, the attracting and invariant sets of the networks are obtained. The results in this paper extend and improve the earlier publications. An example is presented to illustrate the effectiveness of our conclusion.

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