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Neural Processing Letters
Erschienen in: Neural Processing Letters 2/2019

10.08.2018

Bifurcation Analysis of Delayed Complex-Valued Neural Network with Diffusions

verfasst von: Tao Dong, Jiaqi Bai, Lei Yang

Erschienen in: Neural Processing Letters | Ausgabe 2/2019

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Abstract

In this paper, a class of delayed complex-valued neural network with diffusion under Dirichlet boundary conditions is considered. By using the properties of the Laplacian operator and separating the neural network into real and imaginary parts, the corresponding characteristic equation of neural network is obtained. Then, the dynamical behaviors including the local stability, the existence of Hopf bifurcation of zero equilibrium are investigated. Furthermore, by using the normal form theory and center manifold theorem of the partial differential equation, the explicit formulae which determine the direction of bifurcations and stability of bifurcating periodic solutions are obtained. Finally, a numerical simulation is carried out to illustrate the results.
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Literatur
1.
2.
Ding X, Cao J, Zhao X et al (2017) Finite-time stability of fractional-order complex-valued neural networks with time delays. Neural Process Lett 46(2):1–20CrossRef
3.
Lee DL (2006) Improvements of complex-valued Hopfield associative memory by using generalized projection rules. IEEE Trans Neural Netw 17(5):1341–1347CrossRef
4.
Gong W, Liang J, Zhang C et al (2016) Nonlinear measure approach for the stability analysis of complex-valued neural networks. Neural Process Lett 44(2):539–554CrossRef
5.
Nitta T (2003) Solving the XOR problem and the detection of symmetry using a single complex-valued neuron. Neural Netw 16(8):1101–1105MathSciNetCrossRef
6.
Hu J, Wang J (2012) Global stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 23(6):853–865CrossRef
7.
Dong T, Liao X, Wang A (2015) Stability and Hopf bifurcation of a complex-valued neural network with two time delays. Nonlinear Dyn 82(1–2):173–184MathSciNetCrossRef
8.
Wang Z, Huang L (2016) Global stability analysis for delayed complex-valued BAM neural networks. Neurocomputing 173:2083–2089CrossRef
9.
Song Q, Zhao Z (2016) Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales. Neurocomputing 171:179–184CrossRef
10.
Dong T, Liao X (2013) Hopf-Pitchfork bifurcation in a simplified BAM neural network model with multiple delays. J Comput Appl Math 253:222–234MathSciNetCrossRef
11.
Li Y, Liao X, Li H (2016) Global attracting sets of non-autonomous and complex-valued neural networks with time-varying delays. Neurocomputing 173:994–1000CrossRef
12.
Dong T, Liao X (2013) Bogdanov–Takens bifurcation in a tri-neuron BAM neural network model with multiple delays. Nonlinear Dyn 71(3):583–595MathSciNetCrossRef
13.
Wang Z, Huang L (2016) Global stability analysis for delayed complex-valued BAM neural networks. Neurocomputing 173:2083–2089CrossRef
14.
Xu W, Cao J, Xiao M et al (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
15.
Li Y (2017) Impulsive synchronization of stochastic neural networks via controlling partial states. Neural Process Lett 46(1):59–69CrossRef
16.
Lu J, Wang Z, Cao J et al (2012) Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay. Int J Bifurc Chaos 22(7):1250176CrossRef
17.
Zhao H, Yuan J, Zhang X (2015) Stability and bifurcation analysis of reaction–diffusion neural networks with delays. Neurocomputing 147:280–290CrossRef
18.
Ren SY, Wu J, Wei PC (2017) Passivity and pinning passivity of coupled delayed reaction–diffusion neural networks with Dirichlet boundary conditions. Neural Process Lett 45(3):869–885CrossRef
19.
Sheng Y, Zeng Z (2017) Synchronization of stochastic reaction–diffusion neural networks with Dirichlet boundary conditions and unbounded delays. Neural Netw 93:89–98CrossRef
20.
Lu JG (2008) Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions. Chaos Solitons Fractals 35(1):116–125MathSciNetCrossRef
21.
Li R, Cao J (2016) Stability analysis of reaction–diffusion uncertain memristive neural networks with time-varying delays and leakage term. Appl Math Comput 278:54–69MathSciNetMATH
22.
Zheng CD, Zhang Y, Wang Z (2014) Stability analysis of stochastic reaction–diffusion neural networks with Markovian switching and time delays in the leakage terms. Int J Mach Learn Cybern 5(1):3–12CrossRef
23.
Tian X, Xu R, Gan Q (2015) Hopf bifurcation analysis of a BAM neural network with multiple time delays and diffusion. Appl Math Comput 266:909–926MathSciNetMATH
24.
Tian X, Xu R (2017) Stability and Hopf bifurcation of time fractional Cohen–Grossberg neural networks with diffusion and time delays in leakage terms. Neural Process Lett 45(2):593–614CrossRef
25.
Dong T, Xu W, Liao X (2017) Hopf bifurcation analysis of reaction–diffusion neural oscillator system with excitatory-to-inhibitory connection and time delay. Nonlinear Dyn 89(4):2329–2345MathSciNetCrossRef
26.
Dong T, Xia L (2017) Stability and Hopf bifurcation of a reaction–diffusion neutral neuron system with time delay. Int J Bifurc Chaos 27(14):1250176MathSciNetCrossRef
27.
Ruan S, Wei J (2003) On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dyn Contin Discrete Impuls Syst Series A 10:863–874MathSciNetMATH
28.
Wu J (2012) Theory and applications of partial functional differential equations. Springer, Berlin
Metadaten
Titel
Bifurcation Analysis of Delayed Complex-Valued Neural Network with Diffusions
verfasst von
Tao Dong
Jiaqi Bai
Lei Yang
Publikationsdatum
10.08.2018
Verlag
Springer US
Erschienen in
Neural Processing Letters / Ausgabe 2/2019
Print ISSN: 1370-4621
Elektronische ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-018-9899-0

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