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doi: 10.3934/dcdss.2020359

Further stability analysis of neutral-type Cohen-Grossberg neural networks with multiple delays

Department of Mathematics, Faculty of Science, Istanbul University, Beyazit, Istanbul, Turkey

* Corresponding author: Ozlem Faydasicok

Received  November 2019 Revised  December 2019 Published  May 2020

The key contribution of this paper is to study the stability analysis of neutral-type Cohen-Grossberg neural networks possessing multiple time delays in the states of the neurons and multiple neutral delays in time derivative of states of the neurons. By making the use of a proper Lyapunov functional, we propose a novel sufficient time-independent stability criterion for this model of neutral-type neural networks. The proposed stability criterion in this paper can be absolutely expressed in terms of the parameters of the neural network model considered as this newly proposed criterion only relies on the relationships established among the network parameters. A numerical example is also given to indicate the advantages of the obtained stability criterion over the previously published stability results for the same class of Cohen-Grossberg neural networks. Since obtaining stability conditions for neutral-type Cohen-Grossberg neural networks with multiple delays is a difficult task to achieve, there are only few papers in the literature dealing with this problem. Therefore, the results given in the current paper makes an important contribution to the stability problem for this class of neutral-type neural networks.

Citation: Ozlem Faydasicok. Further stability analysis of neutral-type Cohen-Grossberg neural networks with multiple delays. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020359
References:
[1]

L. O. Chua and L. Yang, Cellular neural networks: Applications, IEEE Trans. Circuits and Systems, 35 (1988), 1273-1290.  doi: 10.1109/31.7601.  Google Scholar

[2]

M. A. Cohen and S. Grossberg, Absolute stability of global pattern formation and parallel memory storage by competitive neural networks, IEEE Trans. Systems Man Cybernet., 13 (1983), 815-826.  doi: 10.1109/TSMC.1983.6313075.  Google Scholar

[3]

J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Nat. Acad. Sci. U.S.A., 79 (1982), 2554-2558.  doi: 10.1073/pnas.79.8.2554.  Google Scholar

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A. GuezV. Protopopsecu and J. Barhen, On the stability, and design of nonlinear continuous neural networks, IEEE Trans. Syst. Man Cybernetics, 18 (1998), 80-87.   Google Scholar

[5]

J. WangY. Cai and J. Yin, Multi-start stochastic competitive Hopfield neural network for frequency assignment problem in satellite communications, Expert Syst. Appl., 38 (2011), 131-145.  doi: 10.1016/j.eswa.2010.06.027.  Google Scholar

[6]

S. C. TongY. M. Li and H. G. Zhang, Adaptive neural network decentralized backstepping output-feedback control for nonlinear large-scale systems with time delays, IEEE Trans. Neural Networks, 22 (2011), 1073-1086.  doi: 10.1109/TNN.2011.2146274.  Google Scholar

[7]

M. GalickiH. WitteJ. DorschelM. Eiselt and G. Griessbach, Common optimization of adaptive preprocessing units and a neural network during the learning period. Application in EEG pattern recognition, Neural Networks, 10 (1997), 1153-1163.  doi: 10.1016/S0893-6080(97)00033-6.  Google Scholar

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Q. ZhuJ. Cao and R. Rakkiyappan, Exponential input-to-state stability of stochastic Cohen-Grossberg neural networks with mixed delays, Nonlinear Dynam., 79 (2015), 1085-1098.  doi: 10.1007/s11071-014-1725-2.  Google Scholar

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Q. Zhu and J. Cao, Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays, IEEE Trans. Neural Netw., 21 (2010), 1314-1325.  doi: 10.1109/TNN.2010.2054108.  Google Scholar

[10]

R. ManivannanR. SamiduraiJ. CaoA. Alsaedi and F. E. Alsaadi, Stability analysis of interval time-varying delayed neural networks including neutral time-delay and leakage delay, Chaos Solitons Fractals, 114 (2018), 433-445.  doi: 10.1016/j.chaos.2018.07.041.  Google Scholar

[11]

Q. Zhu and J. Cao, Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays, IEEE Trans. Neural Netw. Learn. Syst., 23 (2012), 467-479.  doi: 10.1109/TNNLS.2011.2182659.  Google Scholar

[12]

Q. SongQ. YuZ. ZhaoY. Liu and F. E. Alsaadi, Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties, Neural Networks, 103 (2018), 55-62.  doi: 10.1016/j.neunet.2018.03.008.  Google Scholar

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Q. Zhu and X. Li, Exponential and almost sure exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networks, Fuzzy Sets and Systems, 203 (2012), 74-94.  doi: 10.1016/j.fss.2012.01.005.  Google Scholar

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Q. Zhu, Stability analysis of stochastic delay differential equations with Lévy noise, Systems Control Lett., 118 (2018), 62-68.  doi: 10.1016/j.sysconle.2018.05.015.  Google Scholar

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W. Xie and Q. Zhu, Mean square exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networks with expectations in the coefficients, Neurocomputing, 166 (2015), 133-139.  doi: 10.1016/j.neucom.2015.04.020.  Google Scholar

[16]

X. TanJ. Cao and X. Li, Leader-following mean square consensus of stochastic multi-agent systems with input delay via event-triggered control, IET Control Theory Appl., 12 (2018), 299-309.  doi: 10.1049/iet-cta.2017.0462.  Google Scholar

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Q. Zhu and J. Cao, Exponential stability analysis of stochastic reactiondiffusion Cohen-Grossberg neural networks with mixed delays, Neurocomputing, 74 (2011), 3084-3091.  doi: 10.1016/j.neucom.2011.04.030.  Google Scholar

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Q. Zhu and J. Cao, $p$th moment exponential synchronization for stochastic delayed Cohen-Grossberg neural networks with Markovian switching, Nonlinear Dynam., 67 (2012), 829-845.  doi: 10.1007/s11071-011-0029-z.  Google Scholar

[19]

C. GeC. Hua and X. Guan, New delay-dependent stability criteria for neural networks with time-varying delay using delay-decomposition approach, IEEE Trans. Neural Netw. Learn. Syst., 25 (2014), 1378-1383.  doi: 10.1109/TNNLS.2013.2285564.  Google Scholar

[20]

Z. Wang, L. Liu, Q. H. Shan and H. Zhang, Stability criteria for recurrent neural networks with time-varying delay based on secondary delay partitioning method, IEEE Trans. Neural Netw. Learn. Syst., 26 (2015), 2589–2595, . doi: 10.1109/TNNLS.2014.2387434.  Google Scholar

[21]

X. ZhangX. LiJ. Cao and F. Miaadi, Design of memory controllers for finite-time stabilization of delayed neural networks with uncertainty, J. Franklin Inst., 355 (2018), 5394-5413.  doi: 10.1016/j.jfranklin.2018.05.037.  Google Scholar

[22]

I. StamovaT. Stamov and X. Li, Global exponential stability of a class of impulsive cellular neural networks with supremums, Internat. J. Adapt. Control Signal Process., 28 (2014), 1227-1239.  doi: 10.1002/acs.2440.  Google Scholar

[23]

Q. ZhuR. Rakkiyappan and A. Chandrasekar, Stochastic stability of Markovian jump BAM neural networks with leakage delays and impulse control, Neurocomputing, 136 (2014), 136-151.  doi: 10.1016/j.neucom.2014.01.018.  Google Scholar

[24]

H. ChenP. ShiC. C. Lim and P. Hu, Exponential stability for neutral stochastic Markov systems with time-varying delay and its applications, IEEE Trans. Cybernetics, 46 (2016), 1350-1362.  doi: 10.1109/TCYB.2015.2442274.  Google Scholar

[25]

L. ChengZ. G. Hou and M. Tan, A neutral-type delayed projection neural network for solving nonlinear variational inequalities, IEEE Trans. Circuits Syst. II: Express Briefs, 55 (2008), 806-810.  doi: 10.1109/TCSII.2008.922472.  Google Scholar

[26]

S. I. Niculescu, Delay Effects on Stability: A Robust Control Approach, Lecture Notes in Control and Information Sciences, 269, Springer-Verlag, London, 2001. doi: 10.1007/1-84628-553-4.  Google Scholar

[27] V. B. Kolmanovski${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i} }}$ and V. R. Nosov, Stability of Functional-Differential Equations, Mathematics in Science and Engineering, 180, Academic Press, Inc., London, 1986.   Google Scholar
[28] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Mathematics in Science and Engineering, 191, Academic Press, Inc., Boston, MA, 1993.   Google Scholar
[29]

K. ShiH. ZhuS. ZhongY. Zeng and Y. Zhang, New stability analysis for neutral type neural networks with discrete and distributed delays using a multiple integral approac, J. Franklin Inst., 352 (2015), 155-176.  doi: 10.1016/j.jfranklin.2014.10.005.  Google Scholar

[30]

S. MuralisankarA. Manivannan and P. Balasubramaniam, Mean square delay dependent-probability-distribution stability analysis of neutral type stochastic neural networks, ISA Trans., 58 (2015), 11-19.  doi: 10.1016/j.isatra.2015.03.004.  Google Scholar

[31]

H. ChenY. Zhang and P. Hu, Novel delay-dependent robust stability criteria for neutral stochastic delayed neural networks, Neurocomputing, 73 (2010), 2554-2561.  doi: 10.1016/j.neucom.2010.06.003.  Google Scholar

[32]

S. LakshmananJ. H. ParkH. Y. JungO. M. Kwon and R. Rakkiyappan, A delay partitioning approach to delay-dependent stability analysis for neutral type neural networks with discrete and distributed delays, Neurocomputing, 111 (2013), 81-89.  doi: 10.1016/j.neucom.2012.12.016.  Google Scholar

[33]

W. HuQ. Zhu and H. R. Karimi, Some improved Razumikhin stability criteria for impulsive stochastic delay differential systems, IEEE Trans. Automat. Control, 64 (2019), 5207-5213.  doi: 10.1109/TAC.2019.2911182.  Google Scholar

[34]

S. DharaniR. Rakkiyappan and J. Cao, New delay-dependent stability criteria for switched Hopfield neural networks of neutral type with additive time-varying delay components, Neurocomputing, 151 (2015), 827-834.  doi: 10.1016/j.neucom.2014.10.014.  Google Scholar

[35]

K. ShiS. ZhongH. ZhuX. Liu and Y. Zeng, New delay-dependent stability criteria for neutral-type neural networks with mixed random time-varying delays, Neurocomputing, 168 (2015), 896-907.  doi: 10.1016/j.neucom.2015.05.035.  Google Scholar

[36]

G. ZhangT. WangT. Li and S. Fei, Multiple integral Lyapunov approach to mixed-delay-dependent stability of neutral neural networks, Neurocomputing, 275 (2018), 1782-1792.  doi: 10.1016/j.neucom.2017.10.021.  Google Scholar

[37]

H. HuangQ. Du and X. Kang, Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays, ISA Trans., 52 (2013), 759-767.  doi: 10.1016/j.isatra.2013.07.016.  Google Scholar

[38]

X. LiaoY. LiuH. Wang and T. Huang, Exponential estimates and exponential stability for neutral-type neural networks with multiple delays, Neurocomputing, 149 (2015), 868-883.  doi: 10.1016/j.neucom.2014.07.048.  Google Scholar

[39]

Q. Zhu, Stabilization of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control, IEEE Trans. Automat. Control, 64 (2019), 3764-3771.  doi: 10.1109/TAC.2018.2882067.  Google Scholar

[40]

S. Arik, An analysis of stability of neutral-type neural systems with constant time delays, J. Franklin Inst., 351 (2014), 4949-4959.  doi: 10.1016/j.jfranklin.2014.08.013.  Google Scholar

[41]

C. H. LienK. W. YuY. F. LinY. J. Chung and L. Y. Chung, Global exponential stability for uncertain delayed neural networks of neutral type with mixed time delays, IEEE Trans. Syst. Man Cybernetics-PART B: Cybernetics, 38 (2008), 709-720.  doi: 10.1109/TSMCB.2008.918564.  Google Scholar

[42]

Y. YangT. Liang and X. Xu, Almost sure exponential stability of stochastic Cohen-Grossberg neural networks with continuous distributed delays of neutral type, Optik, 126 (2015), 4628-4635.  doi: 10.1016/j.ijleo.2015.08.099.  Google Scholar

[43]

R. Samli and S. Arik, New results for global stability of a class of neutral-type neural systems with time delays, Appl. Math. Comput., 210 (2009), 564-570.  doi: 10.1016/j.amc.2009.01.031.  Google Scholar

[44]

Z. Orman, New sufficient conditions for global stability of neutral-type neural networks with time delays, Neurocomputing, 97 (2012), 141-148.  doi: 10.1016/j.neucom.2012.05.016.  Google Scholar

[45]

C. J. ChengT. L. LiaoJ. J. Yan and C. C. Hwang, Globally asymptotic stability of a class of neutral-type neural networks with delays, IEEE Trans. Syst. Man Cybernetics-PART B: Cybernetics, 36 (2008), 1191-1195.  doi: 10.1109/TSMCB.2006.874677.  Google Scholar

[46]

H. AkcaV. Covachev and Z. Covacheva, Global asymptotic stability of Cohen-Grossberg neural networks of neutral type, J. Math. Sci. (N.Y.), 205 (2015), 719-732.  doi: 10.1007/s10958-015-2278-8.  Google Scholar

[47]

N. Ozcan, New conditions for global stability of neutral-type delayed Cohen-Grossberg neural networks, Neural Networks, 106 (2018), 1-7.  doi: 10.1016/j.neunet.2018.06.009.  Google Scholar

[48]

N. Ozcan, Stability analysis of Cohen-Grossberg neural networks of neutral-type: Multiple delays case, Neural Networks, 113 (2019), 20-27.  doi: 10.1016/j.neunet.2019.01.017.  Google Scholar

show all references

References:
[1]

L. O. Chua and L. Yang, Cellular neural networks: Applications, IEEE Trans. Circuits and Systems, 35 (1988), 1273-1290.  doi: 10.1109/31.7601.  Google Scholar

[2]

M. A. Cohen and S. Grossberg, Absolute stability of global pattern formation and parallel memory storage by competitive neural networks, IEEE Trans. Systems Man Cybernet., 13 (1983), 815-826.  doi: 10.1109/TSMC.1983.6313075.  Google Scholar

[3]

J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Nat. Acad. Sci. U.S.A., 79 (1982), 2554-2558.  doi: 10.1073/pnas.79.8.2554.  Google Scholar

[4]

A. GuezV. Protopopsecu and J. Barhen, On the stability, and design of nonlinear continuous neural networks, IEEE Trans. Syst. Man Cybernetics, 18 (1998), 80-87.   Google Scholar

[5]

J. WangY. Cai and J. Yin, Multi-start stochastic competitive Hopfield neural network for frequency assignment problem in satellite communications, Expert Syst. Appl., 38 (2011), 131-145.  doi: 10.1016/j.eswa.2010.06.027.  Google Scholar

[6]

S. C. TongY. M. Li and H. G. Zhang, Adaptive neural network decentralized backstepping output-feedback control for nonlinear large-scale systems with time delays, IEEE Trans. Neural Networks, 22 (2011), 1073-1086.  doi: 10.1109/TNN.2011.2146274.  Google Scholar

[7]

M. GalickiH. WitteJ. DorschelM. Eiselt and G. Griessbach, Common optimization of adaptive preprocessing units and a neural network during the learning period. Application in EEG pattern recognition, Neural Networks, 10 (1997), 1153-1163.  doi: 10.1016/S0893-6080(97)00033-6.  Google Scholar

[8]

Q. ZhuJ. Cao and R. Rakkiyappan, Exponential input-to-state stability of stochastic Cohen-Grossberg neural networks with mixed delays, Nonlinear Dynam., 79 (2015), 1085-1098.  doi: 10.1007/s11071-014-1725-2.  Google Scholar

[9]

Q. Zhu and J. Cao, Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays, IEEE Trans. Neural Netw., 21 (2010), 1314-1325.  doi: 10.1109/TNN.2010.2054108.  Google Scholar

[10]

R. ManivannanR. SamiduraiJ. CaoA. Alsaedi and F. E. Alsaadi, Stability analysis of interval time-varying delayed neural networks including neutral time-delay and leakage delay, Chaos Solitons Fractals, 114 (2018), 433-445.  doi: 10.1016/j.chaos.2018.07.041.  Google Scholar

[11]

Q. Zhu and J. Cao, Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays, IEEE Trans. Neural Netw. Learn. Syst., 23 (2012), 467-479.  doi: 10.1109/TNNLS.2011.2182659.  Google Scholar

[12]

Q. SongQ. YuZ. ZhaoY. Liu and F. E. Alsaadi, Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties, Neural Networks, 103 (2018), 55-62.  doi: 10.1016/j.neunet.2018.03.008.  Google Scholar

[13]

Q. Zhu and X. Li, Exponential and almost sure exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networks, Fuzzy Sets and Systems, 203 (2012), 74-94.  doi: 10.1016/j.fss.2012.01.005.  Google Scholar

[14]

Q. Zhu, Stability analysis of stochastic delay differential equations with Lévy noise, Systems Control Lett., 118 (2018), 62-68.  doi: 10.1016/j.sysconle.2018.05.015.  Google Scholar

[15]

W. Xie and Q. Zhu, Mean square exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networks with expectations in the coefficients, Neurocomputing, 166 (2015), 133-139.  doi: 10.1016/j.neucom.2015.04.020.  Google Scholar

[16]

X. TanJ. Cao and X. Li, Leader-following mean square consensus of stochastic multi-agent systems with input delay via event-triggered control, IET Control Theory Appl., 12 (2018), 299-309.  doi: 10.1049/iet-cta.2017.0462.  Google Scholar

[17]

Q. Zhu and J. Cao, Exponential stability analysis of stochastic reactiondiffusion Cohen-Grossberg neural networks with mixed delays, Neurocomputing, 74 (2011), 3084-3091.  doi: 10.1016/j.neucom.2011.04.030.  Google Scholar

[18]

Q. Zhu and J. Cao, $p$th moment exponential synchronization for stochastic delayed Cohen-Grossberg neural networks with Markovian switching, Nonlinear Dynam., 67 (2012), 829-845.  doi: 10.1007/s11071-011-0029-z.  Google Scholar

[19]

C. GeC. Hua and X. Guan, New delay-dependent stability criteria for neural networks with time-varying delay using delay-decomposition approach, IEEE Trans. Neural Netw. Learn. Syst., 25 (2014), 1378-1383.  doi: 10.1109/TNNLS.2013.2285564.  Google Scholar

[20]

Z. Wang, L. Liu, Q. H. Shan and H. Zhang, Stability criteria for recurrent neural networks with time-varying delay based on secondary delay partitioning method, IEEE Trans. Neural Netw. Learn. Syst., 26 (2015), 2589–2595, . doi: 10.1109/TNNLS.2014.2387434.  Google Scholar

[21]

X. ZhangX. LiJ. Cao and F. Miaadi, Design of memory controllers for finite-time stabilization of delayed neural networks with uncertainty, J. Franklin Inst., 355 (2018), 5394-5413.  doi: 10.1016/j.jfranklin.2018.05.037.  Google Scholar

[22]

I. StamovaT. Stamov and X. Li, Global exponential stability of a class of impulsive cellular neural networks with supremums, Internat. J. Adapt. Control Signal Process., 28 (2014), 1227-1239.  doi: 10.1002/acs.2440.  Google Scholar

[23]

Q. ZhuR. Rakkiyappan and A. Chandrasekar, Stochastic stability of Markovian jump BAM neural networks with leakage delays and impulse control, Neurocomputing, 136 (2014), 136-151.  doi: 10.1016/j.neucom.2014.01.018.  Google Scholar

[24]

H. ChenP. ShiC. C. Lim and P. Hu, Exponential stability for neutral stochastic Markov systems with time-varying delay and its applications, IEEE Trans. Cybernetics, 46 (2016), 1350-1362.  doi: 10.1109/TCYB.2015.2442274.  Google Scholar

[25]

L. ChengZ. G. Hou and M. Tan, A neutral-type delayed projection neural network for solving nonlinear variational inequalities, IEEE Trans. Circuits Syst. II: Express Briefs, 55 (2008), 806-810.  doi: 10.1109/TCSII.2008.922472.  Google Scholar

[26]

S. I. Niculescu, Delay Effects on Stability: A Robust Control Approach, Lecture Notes in Control and Information Sciences, 269, Springer-Verlag, London, 2001. doi: 10.1007/1-84628-553-4.  Google Scholar

[27] V. B. Kolmanovski${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i} }}$ and V. R. Nosov, Stability of Functional-Differential Equations, Mathematics in Science and Engineering, 180, Academic Press, Inc., London, 1986.   Google Scholar
[28] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Mathematics in Science and Engineering, 191, Academic Press, Inc., Boston, MA, 1993.   Google Scholar
[29]

K. ShiH. ZhuS. ZhongY. Zeng and Y. Zhang, New stability analysis for neutral type neural networks with discrete and distributed delays using a multiple integral approac, J. Franklin Inst., 352 (2015), 155-176.  doi: 10.1016/j.jfranklin.2014.10.005.  Google Scholar

[30]

S. MuralisankarA. Manivannan and P. Balasubramaniam, Mean square delay dependent-probability-distribution stability analysis of neutral type stochastic neural networks, ISA Trans., 58 (2015), 11-19.  doi: 10.1016/j.isatra.2015.03.004.  Google Scholar

[31]

H. ChenY. Zhang and P. Hu, Novel delay-dependent robust stability criteria for neutral stochastic delayed neural networks, Neurocomputing, 73 (2010), 2554-2561.  doi: 10.1016/j.neucom.2010.06.003.  Google Scholar

[32]

S. LakshmananJ. H. ParkH. Y. JungO. M. Kwon and R. Rakkiyappan, A delay partitioning approach to delay-dependent stability analysis for neutral type neural networks with discrete and distributed delays, Neurocomputing, 111 (2013), 81-89.  doi: 10.1016/j.neucom.2012.12.016.  Google Scholar

[33]

W. HuQ. Zhu and H. R. Karimi, Some improved Razumikhin stability criteria for impulsive stochastic delay differential systems, IEEE Trans. Automat. Control, 64 (2019), 5207-5213.  doi: 10.1109/TAC.2019.2911182.  Google Scholar

[34]

S. DharaniR. Rakkiyappan and J. Cao, New delay-dependent stability criteria for switched Hopfield neural networks of neutral type with additive time-varying delay components, Neurocomputing, 151 (2015), 827-834.  doi: 10.1016/j.neucom.2014.10.014.  Google Scholar

[35]

K. ShiS. ZhongH. ZhuX. Liu and Y. Zeng, New delay-dependent stability criteria for neutral-type neural networks with mixed random time-varying delays, Neurocomputing, 168 (2015), 896-907.  doi: 10.1016/j.neucom.2015.05.035.  Google Scholar

[36]

G. ZhangT. WangT. Li and S. Fei, Multiple integral Lyapunov approach to mixed-delay-dependent stability of neutral neural networks, Neurocomputing, 275 (2018), 1782-1792.  doi: 10.1016/j.neucom.2017.10.021.  Google Scholar

[37]

H. HuangQ. Du and X. Kang, Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays, ISA Trans., 52 (2013), 759-767.  doi: 10.1016/j.isatra.2013.07.016.  Google Scholar

[38]

X. LiaoY. LiuH. Wang and T. Huang, Exponential estimates and exponential stability for neutral-type neural networks with multiple delays, Neurocomputing, 149 (2015), 868-883.  doi: 10.1016/j.neucom.2014.07.048.  Google Scholar

[39]

Q. Zhu, Stabilization of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control, IEEE Trans. Automat. Control, 64 (2019), 3764-3771.  doi: 10.1109/TAC.2018.2882067.  Google Scholar

[40]

S. Arik, An analysis of stability of neutral-type neural systems with constant time delays, J. Franklin Inst., 351 (2014), 4949-4959.  doi: 10.1016/j.jfranklin.2014.08.013.  Google Scholar

[41]

C. H. LienK. W. YuY. F. LinY. J. Chung and L. Y. Chung, Global exponential stability for uncertain delayed neural networks of neutral type with mixed time delays, IEEE Trans. Syst. Man Cybernetics-PART B: Cybernetics, 38 (2008), 709-720.  doi: 10.1109/TSMCB.2008.918564.  Google Scholar

[42]

Y. YangT. Liang and X. Xu, Almost sure exponential stability of stochastic Cohen-Grossberg neural networks with continuous distributed delays of neutral type, Optik, 126 (2015), 4628-4635.  doi: 10.1016/j.ijleo.2015.08.099.  Google Scholar

[43]

R. Samli and S. Arik, New results for global stability of a class of neutral-type neural systems with time delays, Appl. Math. Comput., 210 (2009), 564-570.  doi: 10.1016/j.amc.2009.01.031.  Google Scholar

[44]

Z. Orman, New sufficient conditions for global stability of neutral-type neural networks with time delays, Neurocomputing, 97 (2012), 141-148.  doi: 10.1016/j.neucom.2012.05.016.  Google Scholar

[45]

C. J. ChengT. L. LiaoJ. J. Yan and C. C. Hwang, Globally asymptotic stability of a class of neutral-type neural networks with delays, IEEE Trans. Syst. Man Cybernetics-PART B: Cybernetics, 36 (2008), 1191-1195.  doi: 10.1109/TSMCB.2006.874677.  Google Scholar

[46]

H. AkcaV. Covachev and Z. Covacheva, Global asymptotic stability of Cohen-Grossberg neural networks of neutral type, J. Math. Sci. (N.Y.), 205 (2015), 719-732.  doi: 10.1007/s10958-015-2278-8.  Google Scholar

[47]

N. Ozcan, New conditions for global stability of neutral-type delayed Cohen-Grossberg neural networks, Neural Networks, 106 (2018), 1-7.  doi: 10.1016/j.neunet.2018.06.009.  Google Scholar

[48]

N. Ozcan, Stability analysis of Cohen-Grossberg neural networks of neutral-type: Multiple delays case, Neural Networks, 113 (2019), 20-27.  doi: 10.1016/j.neunet.2019.01.017.  Google Scholar

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