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Neural Processing Letters

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05-01-2021

Bifurcations Induced by Self-connection Delay in High-Order Fractional Neural Networks

Authors: Chengdai Huang, Jinde Cao

Published in: Neural Processing Letters | Issue 1/2021

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Abstract

This paper discusses the problem of bifurcations for a delayed fractional-order neural networks (FONNs) with multiple neurons. Self-connection delay is carefully viewed as a bifurcation parameter, stability zones and bifurcation conditions are nicely established, respectively. It declares that self-connection delay immensely affects the stability and bifurcation of the developed FONNs. The explored FONNs illustrate preferable stability performance if selecting a lesser self-connection delay, and Hopf bifurcation generates once they overstep the critical values. Moreover, the effects of fractional order on the bifurcation points are fully studied. It detects that the emergence of bifurcation can be lagged as fractional order amplifies. The verification of the feasibility of the developed theory is implemented via numerical experiments.

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Chen ZM, Liu KH, Liu XX, Lou YJ (2020) Modelling epidemics with fractional-dose vaccination in response to limited vaccine supply. J Theor Biol 486:110085MathSciNetCrossRef

Hashemizadeh E, Ebrahimzadeh A (2018) An efficient numerical scheme to solve fractional diffusion-wave and fractional Klein–Gordon equations in fluid mechanics. Physica A 503:1189–1203MathSciNetCrossRef

Liu J, Li P, Chen W, Qin KY, Qi L (2019) Distributed formation control of fractional-order multi-agent systems with relative damping and nonuniform time-delays. ISA Trans 93:189–198CrossRef

Zhang Q, Cui NX, Y. Shang YL, Xing GJ, Zhang CH, (2018) Relevance between fractional-order hybrid model and unified equivalent circuit model of electric vehicle power battery. Sci China Inf Sci 61:070208

Meng B, Wang XH, Zhang ZY, Wang Z (2020) Necessary and sufficient conditions for normalization and sliding mode control of singular fractional-order systems with uncertainties. Sci China Inf Sci 63:152202MathSciNetCrossRef

Lundstrom B, Higgs M, Spain W, Fairhall A (2008) Fractional differentiation by neocortical pyramidal neurons. Nat Neurosci 11:1335–1342CrossRef

Anastassiou G (2012) Fractional neural network approximation. Comput Math Appl 64:1655–1676MathSciNetCrossRef

Gu YJ, Yu YG, Wang H (2017) Synchronization-based parameter estimation of fractional-order neural networks. Physica A 483:351–361MathSciNetCrossRef

Aslipour Z, Yazdizadeh A (2019) Identification of nonlinear systems using adaptive variable-order fractional neural networks. Eng Appl Artif Intell 85:462–473CrossRef

10.

Gu YJ, Wang H, Yu YG (2019) Stability and synchronization for Riemann-Liouville fractional-order time-delayed inertial neural networks. Neurocomputing 340:270–280CrossRef

11.

Fan YJ, Huang X, Wang Z, Li YX (2018) Global dissipativity and quasi-synchronization of asynchronous updating fractional-order memristor-based neural networks via interval matrix method. J Frankl Inst 355:5998–6025MathSciNetCrossRef

12.

Jia J, Huang X, Li YX, Cao JD, Alsaedi A (2020) Global stabilization of fractional-order memristor-based neural networks with time delay. IEEE Trans Neural Netw Learn Syst 31:997–1009MathSciNetCrossRef

13.

Marcus CM, Westervelt RM (1989) Stability of analog neural network with delay. Phys Rev A 39:347–359MathSciNetCrossRef

14.

Tian XH, Xu R, Gan QT (2015) Hopf bifurcation analysis of a BAM neural network with multiple time delays and diffusion. Appl Math Comput 266:909–926MathSciNetMATH

15.

Faydasicok O (2020) A new Lyapunov functional for stability analysis of neutral-type Hopfield neural networks with multiple delays. Neural Netw 129:288–297CrossRef

16.

Zhang JM, Wu JW, Bao HB, Cao JD (2018) Synchronization analysis of fractional-order three-neuron BAM neural networks with multiple time delays. Appl Math Comput 339:441–450MathSciNetCrossRef

17.

Ge JH, Xu J (2018) Stability and Hopf bifurcation on four-neuron neural networks with inertia and multiple delays. Neurocomputing 287:34–44CrossRef

18.

Liang S, Wu RC, Chen LP (2015) Comparison principles and stability of nonlinear fractional-order cellular neural networks with multiple time delays. Neurocomputing 168:618–625CrossRef

19.

Chen LP, Cao JD, Wu RC, Machadod JAT, Lopese AM, Yang HJ (2017) Stability and synchronization of fractional-order memristive neural networks with multiple delays. Neural Netw 94:76–85CrossRef

20.

Zhang WW, Zhang H, Cao JD, Alsaadi FE, Chen DY (2019) Synchronization in uncertain fractional-order memristive complex-valued neural networks with multiple time delays. Neural Netw 110:186–198CrossRef

21.

Cao JD, Guerrini L, Cheng ZS (2019) Stability and Hopf bifurcation of controlled complex networks model with two delays. Appl Math Comput 343:21–29MathSciNetMATH

22.

Tigan G, Lazureanu C, Munteanu F, Sterbeti C, Florea A (2020) Bifurcation diagrams in a class of Kolmogorov systems. Nonlinear Anal Real World Appl 56:103154MathSciNetCrossRef

23.

Jia YT (2020) Bifurcation and pattern formation of a tumor-immune model with time-delay and diffusion. Math Comput Simul 178:92–108MathSciNetCrossRef

24.

Djilali S, Ghanbari B, Bentout S, Mezouaghi A (2020) Turing-Hopf bifurcation in a diffusive mussel-algae model with time-fractional-order derivative. Chaos Solitons Fractals 138:109954MathSciNetCrossRef

25.

Eshaghi S, Ghaziani RK, Ansari A (2020) Hopf bifurcation, chaos control and synchronization of a chaotic fractional-order system with chaos entanglement function. Math Comput Simul 172:321–340MathSciNetCrossRef

26.

Alidousti J (2020) Stability and bifurcation analysis for a fractional prey-predator scavenger model. Appl Math Model 81:342–355MathSciNetCrossRef

27.

Huang CD, Li ZH, Ding DW, Cao JD (2018) Bifurcation analysis in a delayed fractional neural network involving self-connection. Neurocomputing 314:186–197CrossRef

28.

Huang CD, Nie XB, Zhao X, Song QK, Tu ZW, Xiao M, Cao JD (2019) Novel bifurcation results for a delayed fractional-order quaternion-valued neural network. Neural Netw 117:67–93CrossRef

29.

Huang CD, Zhao X, Wang XH, Wang ZX, Xiao M, Cao JD (2019) Disparate delays-induced bifurcations in a fractional-order neural network. J Frankl Inst 356:2825–2846MathSciNetCrossRef

30.

Huang CD, Liu H, Shi XY, Chen XP, Xiao M, Wang ZX, Cao JD (2020) Bifurcations in a fractional-order neural network with multiple leakage delays. Neural Netw 131:115–126CrossRef

31.

Huang CD, Cao JD (2020) Bifurcation mechanisation of a fractional-order neural network with unequal delays. Neural Process Lett 52:1171–1187CrossRef

32.

Alimi AM, Aouiti C, Miaadi F (2019) Effect of leakage delay on finite time boundedness of impulsive high-order neutral delay generalized neural networks. Neurocomputing 347:34–45CrossRef

33.

He ZL, Li CD, Li HF, Zhang QQ (2020) Global exponential stability of high-order Hopfield neural networks with state-dependent impulses. Physica A 542:123434MathSciNetCrossRef

34.

Shen WQ, Zhang X, Wang YT (2020) Stability analysis of high order neural networks with proportional delays. Neurocomputing 372:33–39CrossRef

35.

Huang CD, Cao JD, Xiao M, Alsaedi A, Hayat T (2018) Effects of time delays on stability and Hopf bifurcation in a fractional ring-structured network with arbitrary neurons. Commun Nonlinear Sci Numer Simul 57:1–13MathSciNetCrossRef

36.

Yuan SL, Li XM (2010) Stability and bifurcation analysis of an annular delayed neural network with self-connection. Neurocomputing 73:2905–2912CrossRef

37.

Podlubny I (1999) Fractional differential equations. Academic Press, New YorkMATH

38.

Deng WH, Li CP, Lü JH (2007) linear fractional differential system with multiple time delays. Nonlinear Dyn 48:409–416MathSciNetCrossRef

Title: Bifurcations Induced by Self-connection Delay in High-Order Fractional Neural Networks
Authors: Chengdai Huang
Jinde Cao
Publication date: 05-01-2021
Publisher: Springer US
Published in: Neural Processing Letters / Issue 1/2021
Print ISSN: 1370-4621
Electronic ISSN: 1573-773X
DOI: https://doi.org/10.1007/s11063-020-10395-5

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