In this paper, fuzzy cellular neural networks with distributed delays and variable coefficients are studied. Applying Gaines and Mawhin,s continuation theorem of coincidence degree theory, the method of Lyapunov function and the elementary inequality 2xy ≤ x2 + y2, we establish some sufficient conditions which ensure the existence and global exponential stability of periodic solution of such fuzzy cellular neural networks with distributed delays and variable coefficients. These sufficient conditions, which are easily checked in practice by simple algebra methods, have a wide range of application. An example with its numerical simulations is given to show the feasibility of the obtained theoretical predictions. The results obtained in this article are completely new and complement the previously known studies.
YangT. and YangL., The global stability of fuzzy cellular neural networks, IEEE Transcations on Circuits and Systems43(10) (1996), 880–883.
2.
YangT., YangL., WuC.W. and ChuaL.O., Fuzzy cellular neural networks: Theory, in Proceedings of IEEE Intertional Worksshop on Cellular Neural Network and Applications, 1996, pp. 181–186.
3.
YangT., YangL., WuC.W. and ChuaL.O., Fuzzy cellular neural networks: Applications, in Proceedings of IEEE Intertional Worksshop on Cellular Neural Network and Applications, 1996, 225–230.
4.
BalasubramaniamP., KalpanaM. and RakkiyappanR., Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays, Mathematical and Computer Modelling53(5-6) (2011), 839–853.
5.
DuanL. and HuangL.H., Global exponential stability of fuzzy BAM neural networks with distributed delays and time -varying delays in the leakage terms, Neural Computing and Applications23(1) (2013), 171–178.
6.
Syed AliM. and BalasubramaniamP., Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple discrete and distributed time-varying delays, Communications in Nonlinear Science and Numerical Simulation16(7) (2011), 2907–2916.
7.
LongS.J. and XuD.Y., Global exponential p-stability of stochastic non-autonomous Takagi-Sugeno fuzzy cellular neural networks with time-varying delays and impulses, Fuzzy Sets and Systems253 (2014), 82–100.
8.
SongQ.K. and WangZ.D., Dynamical behaviors of fuzzy reactiondiffusion periodic cellular neural networks with variable coefficients and delays, Applied Mathematical Modelling33(9) (2009), 3533–3545.
9.
HuangT.W., Exponential stability of fuzzy cellular neural networks with distributed delay, Physics Letters A351(1-2) (2006), 48–52.
10.
YangG.W., KaoY.G., Li and W., SunX.Q., Exponential stability of impulsive stochastic fuzzy cellular neural networks with mixed delays and reaction-diffusion terms, Neural Computing and Applications23(3-4) (2013), 1109–1121.
11.
YuanK., CaoJ.D. and DengJ.M., Exponential stability and periodic solutions of fuzzy cellular neural networks with timevarying delays, Neurocomputing69(13-15) (2006), 1619–1627.
12.
LiuY.Q. and TangW.S., Exponential stability of fuzzy cellular neural networks with constant and time-varying delays, Physics Letters A323(3-4) (2004), 224–233.
13.
SongQ.K. and CaoJ.D., Dynamical behaviors of a discrete-time fuzzy cellular neural networks with variable delays and impulses, Journal of the Franklin Institute345(1) (2008), 39–59.
14.
LiuZ.W., ZhangH.G. and WangZ.S., Novel stability criterions of a new fuzzy cellular neural networks with time-varying delays, Neurocomputing72(4-6) (2009), 1056–1064.
15.
TanM., Global asymptotic stability of fuzzy cellular neural networks with unbounded distributed delays, Neural Processing Letters31(2) (2010), 147–157.
16.
LiK., Impulsive effect on global exponential stability of BAM fuzzy cellular neural networkswith time-varying delays, International Journal of Systems Science41(2) (2010), 131–142.
17.
YuF. and JiangH.J., Global exponential synchronization of fuzzy cellular neural networks with delays and reaction-diffusion terms, Neurocomputing74(4) (2011), 509–515.
18.
ZhangQ.H. and XiangR.G., Global asymptotic stability of fuzzy cellular neural networks with time-varying delays, Physics Letters A372(22) (2008), 3971–3977.
19.
ChenL.P., WuR. and PanD.H., Mean square exponential stability of impulsive stochastic fuzzy cellular neural networks with distributed delays, Expert Systems with Applications38(5) (2011), 6294–6299.
20.
RakkiyappanR. and BalasubramaniamP., On exponential stability results for fuzzy impulsive neural networks, Fuzzy Sets and Systems161(13) (2010), 1823–1835.
21.
LiY. and WangC., Existence and global exponential stability of equilibrium for discrete-time fuzzy BAM neural networks with variable delays and impulses, Fuzzy Sets and Systems217 (2013), 62–79.
22.
LiX., RakkiyappanR. and BalasubramaniamP., Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations, Journal of the Franklin Institute348(2) (2011), 135–155.
23.
BalasubramaniamP., KalpanaM. and RakkiyappanR., Stationary oscillation of interval fuzzy cellular neural networks with mixed delays under impulsive perturbations, Neural Computing and Applications22(7-8) (2013), 1645–1654.
24.
HanW., LiuY. and WangL.S., Global exponential stability of delayed fuzzy cellular neural networks with Markovian jumping parameters, Neural Computing and Applications21(1) (2012), 67–72.
25.
CaoJ.D., Global exponential stability and periodic solutions of delayed cellular neural networks, Journal of Computer and Systems Sciences60(1) (2000), 38–46.
26.
CaoJ.D., New results concerning exponential stability and periodic solutions of delayed cellular neural networks, Physics Letters A307(2-3) (2003), 136–147.
27.
CaoJ.D. and LiQ., On the exponential stability and periodic solutions of delayed cellular neural networks, Journal of Mathematical Analysis and Applications252(1) (2000), 50–64.
28.
YanP. and LvT., Exponential syschronization of fuzzy cellular neural networks with mixed delay and general boundary conditions, Communications in Nonlinear Science and Numerical Simulation17(2) (2012), 1003–1011.
29.
LvT. and YanP., Dynamical behaviors of reaction-diffusion fuzzy neural networks with hybrid delays and general boundary conditions, Communications in Nonlinear Science and Numerical Simulation16(2) (2011), 993–1001.
30.
WangJ. and LuJ., Globally exponential stability of fuzzy cellular neural networks with delays and reaction-diffusion terms, Chaos Soliton and Fractals38(3) (2008), 878–885.
31.
HuangT., Exponential stability of delayed fuzzy cellular neural networks with diffusion, Chaos Soliton and Fractals31(3) (2007), 658–664.
32.
HuangT., Exponential stability of fuzzy cellular neural networks with unbounded distributed delay, Physics Letters A351(1-2) (2006), 44–52.
33.
NiuS.Y., JiangH.J. and TengZ.D., Periodic oscillation of FCNNs with distributed delays and variable coefficients, Nonlinear Analysis: Real World Applications10(3) (2009), 1540–1554.
34.
GainesR.E. and MawhinJ.L., Coincidence Degree and Nonlinear Differential Equations, Springer-verlag, Berlin, 1997.
35.
LiaoX.F. and YuJ.B., Qualitative analysis of bi-directional associative memory with time delay, International Journal of Circuit Theory and Applications26(3) (1998), 219–229.
36.
OtadiM. and MoslehM., Simulation and evaluation of intervalvalued fuzzy linear Fredholm integral equations with intervalvalued fuzzy neural network, Neurocomputing205 (2016), 519–528.
37.
AbdurahmanA. and JiangH.J., TengZ.D., Finite-time synchronization for fuzzy cellular neural networks with time-varying delays, Fuzzy Sets and Systems297 (2016), 96–111.
38.
MoslehM. and OtadiM., Numerical solutions of nonlinear fuzzy Fredholm integro-differential equations of the second kind, Iranian Journal of Fuzzy Systems12(2) (2015), 117–127.
