In this paper, a class of fuzzy cellular neural networks with proportional delays are considered. Applying the differential inequality theory and constructing Lyapunov functional, some sufficient criteria which ensure the global exponential periodicity of fuzzy cellular neural networks with proportional delays are established. Numerical simulations are carried out to illustrate our theoretical predictions. Compared with the previous works, the main contributions lies in: (1) it is the first to deal with the global exponential periodicity of fuzzy cellular neural networks with proportional delays; (2) some new sufficient criteria to ensure the global exponential periodicity of fuzzy cellular neural networks with proportional delays are established; (3) the obtained results of this paper are new and complement some existing ones.
BanJ.C. and ChangC.H., When are two multi-layer cellular neural networks the same?Neural Networks79 (2016), 12–19.
2.
WangL.X., ZhangJ.M. and ShaoH.J., Existence and global stability of a periodic solution for a cellular neural network, Communications in Nonlinear Science and Numerical Simulation19(9) (2014), 2983–2992.
3.
HuangC.X., CaoJ. and CaoJ.D., Stability analysis of switched cellular neural networks: A mode-dependent average dwell time approach, Neural Networks82 (2016), 84–99.
4.
SongQ.K., YanH., ZhaoZ.J. and LiuY.R., Global exponential stability of complex-valued neural networks with both timevarying delays and impulsive effects, Neural Networks79 (2016), 108–116.
5.
StamovaI.M. and IlarionovR., On global exponential stability for impulsive cellular neural networks with time-varying delays, Computers & Mathematics with Applications59(11) (2010), 3508–3515.
6.
TyagiS., AbbasS., PintoM. and SepúlvedaD., Uniform Euler approximation of solutions of fractional-order delayed cellular neural network on bounded intervals, Computers & Mathematics with Applications (2016). In press.
7.
AbdurahmanA., JiangH.J. and TengZ.D., Finite-time synchronization for fuzzy cellular neural networks with time-varying delays, Fuzzy Sets and Systems297 (2016), 96–111.
8.
WangP., LiB. and LiY.K., Square-mean almost periodic solutions for impulsive stochastic shunting inhibitory cellular neural networks with delays, Neurocomputing167 (2015), 76–82.
9.
RakkiyappanR., SakthivelN., ParkJ.H. and KwonO.M., Sampleddata state estimation for Markovian jumping fuzzy cellular neural networks with mode-dependent probabilistic time-varying delays, Applied Mathematics and Computation221 (2013), 741–769.
10.
BalasubramaniamP., KalpanaM. and RakkiyappanR., Existence and global asymptotic stability of fuzzy cellular neural networks with time delay in the leakage term and unbounded distributed delays, Circuits, Systems, and Signal Processing30(6) (2011), 1595–1616.
11.
QinS.T., WangJ. and XueX.P., Convergence and attractivity of memristor-based cellular neural networks with time delays, Neural Networks63 (2015), 223–233.
12.
SongX.L., XinX. and HuangW.P., Exponential stability of delayed and impulsive cellular neural networks with partially Lipschitz continuous activation functions, Neural Networks29-30 (2012), 80–90.
13.
GaoJ., WangQ.R. and ZhangL.W., Existence and stability of almost-periodic solutions for cellular neural networks with timevarying delays in leakage terms on time scales, Applied Mathematics and Computation237 (2014), 639–649.
14.
LiY.K. and WangC., Almost periodic solutions of shunting inhibitory cellular neural networks on time scales, Communications in Nonlinear Science and Numerical Simulation17(8) (2012), 3258–3266.
15.
YuY.H., Global exponential convergence for a class of HCNNs with neutral time-proportional delays, Applied Mathematics and Computation285 (2016), 1–7.
16.
YaoL.G., Global exponential convergence of neutral type shunting inhibitory cellular neural networks with D operator, Neural Processing Letters (2016). In press.
17.
XuC.J. and WuY.S., On almost automorphic solutions for cellula neural networks with time-varying delays in leakage terms on time scales, Journal of Intelligent and Fuzzy Systems30 (2016), 423–436.
18.
XuC.J., ZhangQ.M. and WuY.S., Existence and exponential stability of periodic solution to fuzzy cellular neural networks with distributed delays, International Journal of Fuzzy Systems18(1) (2016), 41–51.
19.
XuC.J., LiP.L. and PangY.C., Exponential stability of almost periodic solutions for memristor-based neural networks with distributed leakage delays, Neural Computation28(12) (2016), 2726–2756.
20.
XuC.J., Existence and exponential stability of anti-periodic solution in cellular neural networks with time-varying delays and impulsive effects, Electronic Journal of Differential Equations2016(2) (2016), 1–14.
21.
BalasubramaniamP., AliM.S. and ArikS., Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple time-varying delays, Expert Systems with Applications37(12) (2010), 7737–7744.
22.
BalasubramaniamP., KalpanaM. and RakkiyappanR., Existence and global asymptotic stability of fuzzy cellular neural networks with time dealy in the leakage term and unbounded distributed delays, Circuits, Systems, and Signal Processing30(6) (2011), 1595–1616.
23.
YangW.G., Periodic solution for fuzzy Cohen-Grossberg BAM neural networks with both time-varying and distributed delays and variable coefficients, Neural Process Letters40(1) (2014), 51–73.
24.
XuC.J. and LiP.L., Existence and exponentially stability of antiperiodic solutions for neutral BAM neural networks with timevarying delays in the leakage terms, Journal of Nonliner Sciecne and Applications9(3) (2016), 1285–1305.
25.
XuC.J., ZhangQ.M. and WuY.S., Existence and stability of pseudo almost periodic solutions for shunting inhibitory cellular neural networks with neutral type delays and time-varying leakage delays, Network: Computation in Neural Systems25(4) (2014), 168–192.
26.
SongQ.K. and ZhaoZ.J., Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales, Neurocomputing171 (2016), 179–184.
27.
SenthilrajS., RajaR., ZhuQ.X., SamiduraiR. and YaoZ.S., Exponential passivity analysis of stochastic neural networks with leakage, distributed delays and Markovian jumping parameters, Neurocomputing175 (2016), 401–410.
28.
RakkiyappanR., LakshmananS., SivasamyR. and LimC.P., Leakage-delay-dependent stability analysis of Markovian jumping linear systems with time-varying delays and nonlinear perturbations, Applied Mathematical Modelling40(7-8) (2016), 5026–5043.
29.
LiY.K., YangL. and WuW.Q., Anti-periodic solution for impulsive BAM neural networks with time-varying leakage delays on time scales, Neurocomputing149 (2015), 536–545.
30.
LiuB.W., Global exponential stability for BAM neural networks with time-varying delays in the leakage terms, Nonlinear Analysis: Real World Applications14(1) (2013), 559–566.
31.
BalasubramanianmP., VembarasanV. and RakkiyappanR., Leakage delay in T-S Fuzzy cellular neural networks, Neural Processing Letters33 (2011), 111–136.
32.
OckendonJ.R. and TaylerA.B., The dynamics of a current collection system for an electric locomotive, Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences322(1551) (1971), 447–468.
33.
SongX.L., ZhaoP., XingZ.W. and PengJ.G., Global asymptotic stability of CNNs with impulses and multi-proportional delays, Mathematical Methods in the Applied Sciences39(4) (2016), 722–733.
34.
DerfelG.A., On the behaviour of the solutions of functional and functional-differential equations with serveral deviating arguments, Ukrainian Mathematical Journal34 (1982), 286–291.
35.
FoxL., OckendonD.F. and TaylerA.B., On a functionaldifferential equations, Journal of the Institutetute of Mathematics and its Applications8(3) (1971), 271–307.
36.
DerfelG.A., Kato problem for functional-differential equations and difference Schrodinger operator, Operator Theory46 (1990), 319–321.
37.
ZhouL.Q. and HuG.D., Global exponential periodicity and stability of cellular neural networks with variable and distributed delays, Applied Mathematics and Computation195(2) (2008), 402–411.
38.
YangT. and YangL.B., The global stability of fuzzy cellular neural networks, IEEE Transactions on Circuits and System I43(10) (1996), 880–883.
39.
HuangZ.D., Almost periodic solutions for fuzzy cellular neural networks with time-varying dealys, Neural Computation and Applications (2016). In press.
40.
HuangZ.D., Almost periodic solutions for fuzzy cellular neural networks with multi-proportional delays, International Journal of Machine Learning and Cybernetics78(4) (2016), 1–8.
41.
LiuY.J., TongS., LiD.J. and GaoY., Fuzzy adaptive control with state observer for a class of nonlinear discrete-time systems with input constraint, IEEE Transactions on Fuzzy Systems24(5) (2016), 1147–1158.
42.
ChenC.L., LiuY.J. and WenG.X., Fuzzy neural network-based adaptive control for a class of uncertain nonlinear stochastic systems, IEEE Transactions on Cybernetics44(5) (2014), 583–593.
43.
LiuY.J. and TongS.C., Adaptive fuzzy control for a class of nonlinear discrete-time systems with backlash, IEEE Transactions on Fuzzy Systems22(5) (2014), 1359–1365.
44.
LiuY.J. and TongS.C., Barrier Lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems, Automatica76 (2017), 143–152.
45.
TongS., ZhangL. and LiY., Observed-based adaptive fuzzy decentralized tracking control for switched uncertain nonlinear large-scale systems with dead zones, IEEE Transactions on Systems, Man, and Cybernetics46(1) (2016), 37–47.
46.
DovrolisC., StiliadisD. and RamanathanP., Proportional differentiated services: Delay differentiation and packet scheduling, IEEE/ACM Transactions on Networking10(1) (2002), 12–26.
