Stability and Hopf Bifurcation Analysis of an (n + m)-Neuron Double-Ring Neural Network Model with Multiple Time Delays

2021 ◽  
Author(s):  
Ruitao Xing ◽  
Min Xiao ◽  
Yuezhong Zhang ◽  
Jianlong Qiu
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Network Model ◽  
Neural Network Model ◽  
Bifurcation Analysis ◽  
Time Delays ◽  
Multiple Time ◽  
Double Ring ◽  
Multiple Time Delays ◽  
Ring Neural Network

scholarly journals Global Stability, Bifurcation, and Chaos Control in a Delayed Neural Network Model

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Amitava Kundu ◽  
Pritha Das
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Neural Network Model ◽  
Bifurcation Analysis ◽  
Time Delays ◽  
Chaos Control ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
The Neural Network

Conditions for the global asymptotic stability of delayed artificial neural network model of n (≥3) neurons have been derived. For bifurcation analysis with respect to delay we have considered the model with three neurons and used suitable transformation on multiple time delays to reduce it to a system with single delay. Bifurcation analysis is discussed with respect to single delay. Numerical simulations are presented to verify the analytical results. Using numerical simulation, the role of delay and neuronal gain parameter in changing the dynamics of the neural network model has been discussed.

QUALITATIVE ANALYSIS OF A NEURAL NETWORK MODEL WITH MULTIPLE TIME DELAYS

1999 ◽  
Vol 09 (08) ◽  
pp. 1585-1595 ◽  
Author(s):  
SUE ANN CAMPBELL ◽  
SHIGUI RUAN ◽  
JUNJIE WEI
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Neural Network Model ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Multiple Time ◽  
Local Stability Analysis ◽  
Multiple Time Delays ◽  
Transcendental Functions

We consider a simplified neural network model for a ring of four neurons where each neuron receives two time delayed inputs: One from itself and another from the previous neuron. Local stability analysis of the positive equilibrium leads to a characteristic equation containing products of four transcendental functions. By analyzing the equivalent system of four scalar transcendental equations, we obtain sufficient conditions for the linear stability of the positive equilibrium. Furthermore, we show that a Hopf bifurcation can occur when the positive equilibrium loses stability.

Complex Dynamics of Discrete-Time Ring Neural Networks

2021 ◽  
Vol 31 (08) ◽  
pp. 2150116
Author(s):  
Xiaoying Wu ◽  
Yuanlong Chen ◽  
Liangliang Li ◽  
Fen Wang
Keyword(s):  
Neural Network ◽  
Discrete Time ◽  
Difference Equations ◽  
Time Delays ◽  
Complex Dynamics ◽  
Multiple Time ◽  
Chaotic Neural Network ◽  
Multiple Time Delays ◽  
Ring Neural Network ◽  
Theoretical Results

This paper mainly considers the complex dynamics of a discrete-time ring neural network with multiple time delays. By transforming the network system into a system of difference equations, one can obtain a chaotic neural network. More specifically, by projection method one can determine a closed invariant set of the system governed by some difference equations, and prove that some invariant subsystem is topologically conjugate to the two-sided symbolic dynamical system. Moreover, numerical simulations are presented to verify the theoretical results.

scholarly journals Dynamical Behavior in a Four-Dimensional Neural Network Model with Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Changjin Xu ◽  
Peiluan Li
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Network Model ◽  
Neural Network Model ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Normal Form Theory ◽  
Form Theory ◽  
Explicit Formulae ◽  
Delay Differential

A four-dimensional neural network model with delay is investigated. With the help of the theory of delay differential equation and Hopf bifurcation, the conditions of the equilibrium undergoing Hopf bifurcation are worked out by choosing the delay as parameter. Applying the normal form theory and the center manifold argument, we derive the explicit formulae for determining the properties of the bifurcating periodic solutions. Numerical simulations are performed to illustrate the analytical results.

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