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Existence of Periodic Solution for Fuzzy Cellular
Neural Networks with Time-Varying Delays
Qianhong Zhang 1,* , Lihui Yang 2 , and Daixi Liao 3
1 Guizhou Key Laboratory of Economics System Simulation,
Guizhou College of Finance and Economics, Guiyang, Guizhou 550004, P.R. China
Tel.: +86 851 6902456
2 Department of Mathematics, Hunan City University, Yiyang, Hunan 413000,
P.R. China
3 Basic Science Department, Hunan Institute of Technology,
Hengyang, Hunan 421002, P.R. China
zqianhong68@163.com, ll.hh.yang@gmail.com,
liaodaixizaici@sohu.com
Abstract. In this paper, by employing continuation theorem of coincidence
degree, and inequality technique, some sufficient conditions are derived to
ensure the existence of periodic solution for fuzzy cellular neural networks with
time-varying delays. These results have important leading significance in the
design and applications of neural networks.
Keywords: Fuzzy cellular neural networks, Periodic solution, Coincidence
degree, Time-varying delays.
1 Introduction
It is well known that fuzzy cellular neural networks is first introduced by Yang and
Yang [1]. Researchers have founded that FCNNs are useful in image processing, and
some results have been reported on stability and periodicity of FCNNs(see, for
example,[1]-[10]). However, to the best of our knowledge, few author investigated the
existence of periodic solution for fuzzy cellular neural networks with time-varying
delays. In this paper, we investigate the following system
n
n
xt ctxt atfxt
()
=−
() ()
+
()
( ())
+∧
α
() ( (
tfxt t It
τ
()))
+
()
i
i
i
ij
j
j
ij
j
ij
i
j
=
1
j
=
1
n
n
n
+∨
β
()
tfxt t
( (
τ
()))
+∧
Ttut Htut
() ()
+∨
() ()
(1)
ij
j
j
ij
ij
j
ij
j
j
=
1
j
=
1
j
=
1
where n corresponds to the number of neurons in neural networks.
* Corresponding author.
i
=
1, 2,
,
n
,
 
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