Stability and Hopf bifurcation of a three-layer neural network model with delays

2016 ◽  
Vol 175 ◽  
pp. 355-370 ◽  
Author(s):  
Zunshui Cheng ◽  
Dehao Li ◽  
Jinde Cao
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Network Model ◽  
Neural Network Model

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.

STABILITY AND BIFURCATION ANALYSIS ON A DELAYED NEURAL NETWORK MODEL

2005 ◽  
Vol 15 (09) ◽  
pp. 2883-2893 ◽  
Author(s):  
XIULING LI ◽  
JUNJIE WEI
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Network Model ◽  
Neural Network Model ◽  
Center Manifold ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory ◽  
Delayed Neural Network ◽  
The Stability

A simple delayed neural network model with four neurons is considered. Linear stability of the model is investigated by analyzing the associated characteristic equation. It is found that Hopf bifurcation occurs when the sum of four delays varies and passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. An example is given and numerical simulations are performed to illustrate the obtained results. Meanwhile, the bifurcation set is provided in the appropriate parameter plane.

scholarly journals Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays

2006 ◽  
Vol 2006 ◽  
pp. 1-18 ◽  
Author(s):  
Xiang-Ping Yan ◽  
Wan-Tong Li
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Global Existence ◽  
Periodic Solutions ◽  
Network Model ◽  
Neural Network Model ◽  
Multiple Delays ◽  
Global Hopf Bifurcation ◽  
Existence Of Periodic Solutions ◽  
Bam Neural Network

We consider a simplified bidirectional associated memory (BAM) neural network model with four neurons and multiple time delays. The global existence of periodic solutions bifurcating from Hopf bifurcations is investigated by applying the global Hopf bifurcation theorem due to Wu and Bendixson's criterion for high-dimensional ordinary differential equations due to Li and Muldowney. It is shown that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the sum of two delays. Numerical simulations supporting the theoretical analysis are also included.

Dynamic Analysis of Fractional-Order Recurrent Neural Network with Caputo Derivative

2017 ◽  
Vol 27 (12) ◽  
pp. 1750181 ◽  
Author(s):  
Weiqian Wang ◽  
Yuanhua Qiao ◽  
Jun Miao ◽  
Lijuan Duan
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Fractional Order ◽  
Network Model ◽  
Recurrent Neural Network ◽  
Neural Network Model ◽  
Caputo Derivative ◽  
Zero Point ◽  
Order System ◽  
Neural Network Models

In this paper, fractional-order recurrent neural network models with Caputo Derivative are investigated. Firstly, we mainly focus our attention on Hopf bifurcation conditions for commensurate fractional-order network with time delay to reveal the essence that fractional-order equation can simulate the activity of neuron oscillation. Secondly, for incommensurate fractional-order neural network model, we prove the stability of the zero equilibrium point to show that incommensurate fractional-order neural network still converges to zero point. Finally, Hopf bifurcation conditions for the incommensurate fractional-order neural network model are first obtained using bifurcation theory based on commensurate fractional-order system.

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