HOPF Bifurcation of a Fractional Tri-Neuron Network with Different Orders and Leakage Delay

Fractals ◽  
2021 ◽  
Author(s):  
Yangling Wang ◽  
Jinde Cao ◽  
Chengdai Huang
Keyword(s):  
Hopf Bifurcation ◽  
Leakage Delay ◽  
Neuron Network

Time-delay-induced instabilities and Hopf bifurcation analysis in 2-neuron network model with reaction–diffusion term

2018 ◽  
Vol 313 ◽  
pp. 306-315 ◽  
Author(s):  
Swati Tyagi ◽  
Subit K Jain ◽  
Syed Abbas ◽  
Shahlar Meherrem ◽  
Rajendra K Ray
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Network Model ◽  
Bifurcation Analysis ◽  
Reaction Diffusion ◽  
Neuron Network ◽  
Diffusion Term

scholarly journals Effect of Leakage Delay on Hopf Bifurcation in a Fractional BAM Neural Network

2019 ◽  
Vol 29 (06) ◽  
pp. 1950077 ◽  
Author(s):  
Jiazhe Lin ◽  
Rui Xu ◽  
Liangchen Li
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Experimental Studies ◽  
Rank Correlation ◽  
Correlation Coefficients ◽  
Leakage Delay ◽  
Scatter Plots ◽  
Bam Neural Network ◽  
Pass Through ◽  
The Impact

Recently, experimental studies show that fractional calculus can depict the memory and hereditary attributes of neural networks more accurately. In this paper, we introduce temporal fractional derivatives into a six-neuron bidirectional associative memory (BAM) neural network with leakage delay. By selecting two different bifurcation parameters and analyzing corresponding characteristic equations, it is verified that the delayed fractional neural network generates Hopf bifurcation when the bifurcation parameters pass through some critical values. In order to measure how much is the impact of leakage delay on Hopf bifurcation, sensitivity analysis methods, such as scatter plots and partial rank correlation coefficients (PRCCs), are introduced to assess the sensitivity of bifurcation amplitudes to leakage delay. Numerical examples are carried out to illustrate the theoretical results and help us gain an insight into the effect of leakage delay.

Bifurcations due to different delays of high-order fractional neural networks

2021 ◽  
pp. 2150075
Author(s):  
Chengdai Huang ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Fractional Order ◽  
Numerical Experiments ◽  
Critical Values ◽  
Communication Delay ◽  
Leakage Delay ◽  
Bifurcation Parameter ◽  
Stability Performance ◽  
The Stability

This paper expounds the bifurcations of two-delayed fractional-order neural networks (FONNs) with multiple neurons. Leakage delay or communication delay is viewed as a bifurcation parameter, stability zones and bifurcation conditions with respect to them are commendably established, respectively. It declares that both leakage delay and communication delay immensely influence the stability and bifurcation of the developed FONNs. The explored FONNs illustrate superior stability performance if selecting a lesser leakage delay or communication delay, and Hopf bifurcation generates once they overstep their critical values. The verification of the feasibility of the developed analytic results is implemented via numerical experiments.

STABILITY AND BIFURCATION FOR A CLASS OF TRI-NEURON NETWORKS WITH BIDIRECTIONALLY DELAYED CONNECTIONS AND SELF-FEEDBACK

2011 ◽  
Vol 21 (06) ◽  
pp. 1601-1616
Author(s):  
SHAOLIANG YUAN ◽  
XUEMEI LI
Keyword(s):  
Hopf Bifurcation ◽  
Center Manifold ◽  
Sufficient Conditions ◽  
Center Manifold Theory ◽  
Neuron Network ◽  
Normal Form Theory ◽  
Neuron Networks ◽  
Stability And Instability ◽  
Form Theory ◽  
Manifold Theory

In this paper, a tri-neuron network with bidirectionally delay and self-feedback is considered. We derive some sufficient conditions dependent or independent of delays for the local stability and instability of this model. Regarding the self-connection delay as the parameter, the Hopf bifurcation analysis is carried out. The direction and stability of the Hopf bifurcation are worked out by applying the normal form theory and the center manifold theory. An example is given and numerical simulations are presented to illustrate the obtained results.

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