Open Access
Subscription Access
The Existence of Anti-periodic Solution for a Class of Cellular Neural Networks
In this paper, we use the Lyapunov function to establish new results on the existence and uniqueness of antiperiodic solutions for a class of cellular neural networks with time-varying delays and continuously distributed delays of
x1(t)=-di(t)hi(t,xi(t))+∑nj=1 aij(t)fj(xj(t-τij(t)))+∑nj=1 bij(t) ×∫∞0 Kij(s)gj(xj(t-s))ds+Ii(t),i=1,2,...,n.Moreover, we also present an example to illustrate the feasibility and effectiveness of our results.
x1(t)=-di(t)hi(t,xi(t))+∑nj=1 aij(t)fj(xj(t-τij(t)))+∑nj=1 bij(t) ×∫∞0 Kij(s)gj(xj(t-s))ds+Ii(t),i=1,2,...,n.Moreover, we also present an example to illustrate the feasibility and effectiveness of our results.
Keywords
Cellular Neural Networks, Distributed Delays, Anti-periodic Solution, Exponential Stability, Delays
User
Information
- Cao J and Wang J (2005) Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans. Circ. Syst. I. 52 (2) 417-426.
- Chen YM (2002) Global stability of neural networks with distributed delays. Neural Networks.15, 867-871.
- Cheng CY, Lin KH and Shih CW (2006) Multi stability in recurrent neural networks. SIAM J.Appl. Math. 66 (4), 1301-1320.
- Chua LO and Yang L (1988) Cellular neural networks: theory and applications. IEEE Trans.Circ. Syst. 35, 1257-1290.
- Hale JK (1977) Theory of functional differential equations. Springer-Verlag, NY.
- Johnson CR and Smith RL (1996) The completion problem for M-matrices and inverse M-matrices, linear algebra and its applications. Lin. Alg. Appl. 241-243, 655-667.
- Li Y (2004) Global stability and existence of periodicsolutions of discrete delayed cellular neural networks. Phy. Lett. A. 333, 51-61.
- Mohamad S (2007) Global exponential stability in DCNNs with distributed delays and unbounded activations. J. Comput. Appl. Math. 205 161-173.
- Peng G and Huang L (2009) Anti-periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays. Nonlin. Anal. 10, 2434-2440.
- Roska T Vandewalle J (1995) Cellular neural networks, Wiley, New York.
- Shao J (2008) Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays. Phy. Lett. A. 372, 5011-5016.
Abstract Views: 479
PDF Views: 92