Bogdanov–Takens bifurcation in a Hopfield network model with bidirectional connection and multiple delays

2015 ◽  
pp. dnv035
Author(s):  
Aws Ben Hamed ◽  
Bassem Ben Hamed
Keyword(s):  
Network Model ◽  
Hopfield Network ◽  
Multiple Delays

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.

Polarization and Non-Positive Social Influence

2012 ◽  
Vol 3 (3) ◽  
pp. 15-25 ◽  
Author(s):  
Zhenpeng Li ◽  
Xijin Tang
Keyword(s):  
Social Identity ◽  
Social Influence ◽  
Numerical Simulations ◽  
Network Model ◽  
Local Structure ◽  
Hopfield Network ◽  
Polarization Pattern ◽  
Dominant State ◽  
External Intervention ◽  
Group Opinion

The authors study patterns about group opinions in a group-based society by considering social influence. They classify three types of social influence: positive, neutral, and negative from the perspective of social identity, and investigate to what extent the non-positive social influence leads to group opinion polarization based on the Hopfield network model. Numerical simulations show that opinion in a group-based society would self-organize into bi-polarization pattern under the condition of no imposing external intervention, which is entirely different from the result of drift to an extreme polarization dominant state with single homogenous influence. These results are explained in the study and the authors show that opinions polarization in a group is coexisted with local structure balance.

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