Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays☆

This Letter is concerned with the existence and exponential stability of anti-periodic solutions for shunting inhibitory cellular neural networks (SICNNs) with time-varying delays arising from the description of the neurons' state in delayed neural networks. Some new sufficient conditions ensuring the existence and exponential stability of anti-periodic solutions for SICNNs are established.

[1]  Jinde Cao,et al.  Almost periodic solution of shunting inhibitory CNNs with delays , 2002 .

[2]  Yuqing Chen,et al.  Anti-periodic solutions for fully nonlinear first-order differential equations , 2007, Math. Comput. Model..

[3]  B. Krauskopf,et al.  Proc of SPIE , 2003 .

[4]  Simeon Reich,et al.  Anti-periodic solutions to nonmonotone evolution equations with discontinuous nonlinearities , 2001 .

[5]  Jinde Cao,et al.  Existence and stability of almost periodic solution for BAM neural networks with delays , 2003, Appl. Math. Comput..

[6]  Sergiu Aizicovici,et al.  On a class of second-order anti-periodic boundary value problems☆ , 1992 .

[7]  Hiroko Okochi,et al.  On the existence of periodic solutions to nonlinear abstract parabolic equations , 1988 .

[8]  Lihong Huang,et al.  Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays , 2006 .

[9]  Yongkun Li,et al.  Global exponential stability of periodic solution for shunting inhibitory CNNs with delays , 2005 .

[10]  Jinde Cao,et al.  On exponential stability and periodic solutions of CNNs with delays , 2000 .

[11]  Jinde Cao,et al.  Almost periodic solution of shunting inhibitory cellular neural networks with time-varying delay , 2003 .

[12]  Bahram Nabet,et al.  Analysis and analog implementation of directionally sensitive shunting inhibitory neural networks , 1991, Defense, Security, and Sensing.

[13]  R. B. Pinter,et al.  Shunting inhibitory cellular neural networks: derivation and stability analysis , 1993 .

[14]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[15]  Jinde Cao,et al.  Almost periodic attractor of delayed neural networks with variable coefficients , 2005 .

[16]  Jinde Cao,et al.  Global exponential stability and periodicity of recurrent neural networks with time delays , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  Zhaohui Yuan,et al.  Positive almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays , 2008, Math. Comput. Simul..

[18]  Jinde Cao,et al.  Periodic oscillation of higher-order bidirectional associative memory neural networks with periodic coefficients and delays , 2007 .