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Neural Processing Letters

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11-09-2018

Stability Switches and Hopf Bifurcation of a Neuron System with both Leakage and Distributed Delays

Authors: Yi Yao, Min Xiao, Jinde Cao, Chengdai Huang, Qiankun Song

Published in: Neural Processing Letters | Issue 1/2019

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Abstract

This paper focuses on the effect of leakage delays on the dynamics of nonlinear delay systems based on a neuron system with discrete and distributed delay. By introducing a virtual neuron, we can eliminate the impact of distributed delay and transform the original neuron system with mixed delays to an equivalent new system involving only discrete delay. This paper extends the existing works on neural networks to the case of leakage delays. We choose the leakage delay as the bifurcation parameter and analyze the role of leakage delays on the stability and Hopf bifurcation. Sufficient conditions for ensuring the neuron system to be stable, and undergoing the Hopf bifurcation are derived. Finally, by using the software package DDE-BIFTOOL, we provide the simulation results to substantiate our theoretical analysis, and give the relationship between the onset of Hopf bifurcation and the system parameters by drawing the bifurcation curves.

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Kosko B (1992) Neural networks and fuzzy systems. Prentice Hall, New DelhiMATH

Wang H, Duan S, Li C, Wang L, Huang T (2017) Exponential stability analysis of delayed memristor-based recurrent neural networks with impulse effects. Neural Comput Appl 28(4):669–678CrossRef

Saravanakumar R, Ali M, Ahn C, Karimi H, Shi P (2017) Stability of markovian jump generalized neural networks with interval time-varying delays. IEEE Trans Neural Netw Learn Syst 28(8):1840–1850MathSciNetCrossRef

Xiao M, Zheng W, Cao J (2013) Frequency domain approach to computational analysis of bifurcation and periodic solution in a two-neuron network model with distributed delays and self-feedbacks. Neurocomputing 99:206–213CrossRef

Xiao M, Zheng W, Jiang G, Cao J (2015) Undamped oscillations generated by Hopf bifurcations in fractional order recurrent neural networks with Caputo derivative. IEEE Trans Neural Netw Learn Syst 26(12):3201–3214MathSciNetCrossRef

Olien L, Bélair J (1997) Bifurcations, stability, and monotonicity properties of a delayed neural network model. Phys D 102(3):349–363MathSciNetCrossRefMATH

Xu W, Cao J, Xiao M, Ho DWC, Wen G (2015) A new framework for analysis on stability and bifurcation in a class of neural networks with discrete and distributed delays. IEEE Trans Cybern 45(10):2224–2236CrossRef

Xiao M, Zheng W, Cao J (2013) Hopf bifurcation of an (\(n+1\))-neuron bidirectional associative memory neural network model with delays. IEEE Trans Neural Netw Learn Syst 24(1):118–132CrossRef

Rakkiyappan R, Dharani S (2017) Sampled-data synchronization of randomly coupled reaction-diffusion neural networks with Markovian jumping and mixed delays using multiple integral approach. Neural Comput Appl 28(3):449–462CrossRef

10.

Sheng Y, Zhang H, Zeng Z (2017) Synchronization of reaction-diffusion neural networks with dirichlet boundary conditions and infinite delays. IEEE Trans Cybern 47(10):3005–3017CrossRef

11.

Li N, Cao J (2018) Synchronization criteria for multiple memristor-based neural networks with time delay and inertial term. Sci China Technol Sci 61(4):612–622MathSciNetCrossRef

12.

Xiao M, Zheng W, Cao J (2013) Bifurcation and control in a neural network with small and large delays. Neural Netw 44:132–142CrossRefMATH

13.

Avitable D, Wedgwood K (2017) Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis. J Math Biol 75(4):885–928MathSciNetCrossRefMATH

14.

Javidmanesh E (2017) Global stability and bifurcation in delayed bidirectional associative memory neural networks with an arbitrary number of neurons. J Dyn Sys Meas Control 139(8):081018CrossRef

15.

Xu C, Zhang Q, Wu Y (2016) Bifurcation analysis in a three-neuron artificial neural network model with distributed delays. Neural Process Lett 44(2):343–373CrossRef

16.

Lai Q, Hu B, Guan Z (2016) Multistability and bifurcation in a delayed neural network. Neurocomputing 207:785–792CrossRef

17.

Xiao M, Zheng W, Jiang G (2018) Bifurcation and oscillatory dynamics of delayed cyclic gene networks including small RNAs. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2017.2789331

18.

Xiao M, Zheng W, Jiang G, Cao J (2016) Stability and bifurcation analysis of arbitrarily high-dimensional genetic regulatory networks with hub structure and bidirectional coupling. IEEE Trans Circuits Syst I, Reg Papers 63(8):1243–1254MathSciNetCrossRef

19.

Haykin S (1999) Neural networks. Prentice Hall, New JerseyMATH

20.

Gopalsamy K (2007) Leakage delays in BAM. J Math Anal Appl 352(2):1117–1132MathSciNetCrossRefMATH

21.

Maharajan C, Raja R, Cao J, Rajchakit G, Tu Z, Alsaedi A (2018) LMI-based results on exponential stability of BAM-type neural networks with leakage and both time-varying delays: a non-fragile state estimation approach. Appl Math Comput 326:33–55MathSciNetMATH

22.

Yang W, Yu W, Cao J, Alsaadi F, Hayat T (2017) Almost automorphic solution for neutral type high-order Hopfield BAM neural networks with time-varying leakage delays on time scales. Neurocomputing 267:241–260CrossRef

23.

Arbi A, Cao J (2017) Pseudo-almost periodic solution on time-space scales for a novel class of competitive neutral-type neural networks with mixed time-varying delays and leakage delays. Neural Process Lett 46(2):719–745CrossRef

24.

Ruan S, Wei J (2003) On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dyn Contin Discr Impuls Syst Ser A 10:863–874MathSciNetMATH

25.

Engelborghs K, Luzyanina T, Roose D (2002) Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL. ACM Trans Math Softw 28(1):1–21MathSciNetCrossRefMATH

Title: Stability Switches and Hopf Bifurcation of a Neuron System with both Leakage and Distributed Delays
Authors: Yi Yao
Min Xiao
Jinde Cao
Chengdai Huang
Qiankun Song
Publication date: 11-09-2018
Publisher: Springer US
Published in: Neural Processing Letters / Issue 1/2019
Print ISSN: 1370-4621
Electronic ISSN: 1573-773X
DOI: https://doi.org/10.1007/s11063-018-9916-3

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