Bifurcation analysis in a delayed fractional neural network involving self-connection

Huang, Chengdai; Li, Zhouhong; Ding, Dawei; Cao, Jinde

doi:10.1016/j.neucom.2018.06.016

Cited by 37 publications

(6 citation statements)

References 29 publications

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“…In details, we refer the readers to previous studies. [42][43][44][45] A natural problem arises: What effect does time delay has on the stability and Hopf bifurcation of fractional-order neural networks? The resolve of this problem will be helpful for us to design neural networks.…”

Section: Introductionmentioning

confidence: 99%

Comparative analysis on Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay

Aouiti

2020

Circuit Theory & Apps

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Summary This article mainly focuses on the stability and the existence of Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay. First of all, we obtain the sufficient criterion to ensure the stability and the existence of Hopf bifurcation of integer‐order two‐neuron neural networks with delay. Next, we establish the sufficient condition guaranteeing the stability and the existence of Hopf bifurcation of fractional‐order two‐neuron neural networks with delay. The study reveals that the time delay has a vital effect on the stability and Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay. By comparative analysis on Hopf bifurcation for integer‐order and fractional‐order two‐neuron neural networks with delay, we find that under an appropriate parameter conditions, the stability region can be enlarged, and the time of appearance of Hopf bifurcation of the involved two‐neuron neural networks can be postponed by using fractional‐order case. Finally, computer simulation results are presented to illustrate the theoretical findings. The established results of this article play an important role in designing and controlling networks.

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Section: Introductionmentioning

confidence: 99%

Comparative analysis on Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay

Aouiti

2020

Circuit Theory & Apps

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“…8, it can be also find that the smaller the order is, the greater the bifurcation point is and the larger the stable domain is. This fact is also true not only for fractional-order neural networks [48], [49], but also for the fractional-order genetic regulatory network [29], the fractional-order predator-prey model [31] and the fractional-order SIS epidemic model [45].…”

Section: Numerical Simulationsmentioning

confidence: 84%

Dynamics of Fractional-Order Neural Networks With Discrete and Distributed Delays

Xiao

Jiang

et al. 2020

IEEE Access

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This paper is concerned with the stability and Hopf bifurcation of fractional-order neural networks with discrete and distributed delays. The novelty of this paper is to take into account the discrete time delay and the distributed time delay for fractional-order systems. By introducing two virtual neurons to the original network, a new four-neuron network only involving discrete delays is formed. The sum of discrete delays is adopted as the bifurcation parameter to demonstrate the existence of Hopf bifurcation. It is found that the critical value of bifurcation can be effectively manipulated by choosing appropriate system parameters and order. Finally, numerical simulations are executed to substantiate the theoretical results and describe the relationships between the parameters and the onset of bifurcation. INDEX TERMS Stability, Hopf bifurcation, discrete delay, distributed delay, fractional-order neural networks.

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“…Thus, it can effectively control the spread of computer viruses or prevent the occurrence of network dangerous events. The research on complex networks is very extensive, including stability and bifurcation of complex networks, which can provide theoretical guidance for our life and production [8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and control of disease spreading networks model with two delays

Cheng

Song

Xiao

2022

Asian Journal of Control

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In this paper, the dynamical behaviors are investigated for a complex network with two independent delays. Instead of taking time delays as bifurcation parameters, we choose probability p$$ p $$ and parameter μ$$ \mu $$ as the control parameters to study their effects on local stability and Hopf bifurcation, respectively. Moreover, the conditions for generating Hopf bifurcation are given. Furthermore, we further discuss the effects of two time delays on the critical values of parameters p$$ p $$ and μ$$ \mu $$. Finally, numerical simulations are used to illustrate the validity of the obtained results.

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Bifurcation analysis in a delayed fractional neural network involving self-connection

Cited by 37 publications

References 29 publications

Comparative analysis on Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay

Comparative analysis on Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay

Dynamics of Fractional-Order Neural Networks With Discrete and Distributed Delays

Bifurcation and control of disease spreading networks model with two delays

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