| 带有变时滞的细胞神经网络模型概周期解的存在性和全局指数稳定性 |
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| 引用本文： | 余连兵.带有变时滞的细胞神经网络模型概周期解的存在性和全局指数稳定性[J].六盘水师范高等专科学校学报,2011,23(3):1-7. |
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| 作者姓名： | 余连兵 |
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| 作者单位： | 六盘水师范学院数学系,贵州 六盘水,530001 |
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| 摘 要： | 应用不动点理论研究了如下的具有变时滞的细胞神经网络模型dxi（t）/dt=-ai（t）xi（t）＋sum from j=1 to nbij（t）fj（xj（t））＋cij（t）fj（xj（xj（t-τj（t）））]＋Ii（t） t≥0,i=1,2,…,n,其中xi（t）（i=1,2,…,n）是神经细胞的状态;n是细胞的数量;B（t）=（bij（t））n×n和C=（cij（t））n×n连续的矩阵函数,I（t）=（I1（t）,I2（t）,…,In（t））T是连续的概周期函数,f（x）=（f1（x1）,f2（x2）,…,fn（xn））T是细胞活动函数,A（t）=diag（a1（t）,a2（t）,…,an（t））,并且ai（t）〉0,（i=1,2,…,n）,时滞0≤τi（t）≤τ（i=1,2,…,n）是有界函数,得出了其概周期解得存在性和全局指数稳定性的充分条件。
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| 关 键 词： | 时滞细胞神经网络 概周期解 不动点定理 重要不等式 |
Existence and Global Exponential Stability of Almost Periodic Solution of Cellular Neural Networks with Variable Delays |
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| SHE Lian-bing.Existence and Global Exponential Stability of Almost Periodic Solution of Cellular Neural Networks with Variable Delays[J].Journal of Liupanshui Teachers College,2011,23(3):1-7. |
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| Authors: | SHE Lian-bing |
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| Institution: | SHE Lian-bing(Department of Mathematics,Liupanshui Normal College,Liupanshui 553001,China) |
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| Abstract: | By using fixed point theorem,some sufficient conditions are obtained for the existence and globally exponential stability of a unique almost periodic solution of a class of neural networks with variable time delays as following form:dxi(t)/dt=-ai(t)xi(t)+sum from j=1 to nbij(t)fj(xj(t))+cij(t)fj(xj(xj(t-τj(t)))]+Ii(t) t≥0,i=1,2,…,n,where xi(t)(i=1,2,…,n) is the state of neuron,andn is the number of neurons;B(t)=(bij(t))n×n and C=(cij(t))n×n,are connection matrix functions,I(t) =(I1(t),I2(t),…,In(t))T is continuously almost periodic functions,f(x)=(f1(x1),f2(x2),…,fn(xn))T is the activation fnnction of the neurons,A(t)=diag(a1(t),a2(t),…,an(t)) with ai(t)>0,(i=1,2,…,n).The delays 0≤τi(t)≤τ(i=1,2,…,n) are bounded functions. |
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| Keywords: | globally exponential stability delayed cellulameural networks almost periodic solution |
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