Existence and stability of periodic solutions for impulsive fuzzy BAM Cohen-Grossberg neural networks on time scales

This paper is concerned with the existence and global exponential stability of periodic solutions for a kind of impulsive fuzzy Cohen-Grossberg BAM neural networks on time scales. Applying the method of coincidence degree and constructing some suitable Lyapunov functional, we obtain some sufficient conditions for the existence and global exponential stability of periodic solutions for a kind of impulsive fuzzy Cohen-Grossberg BAM neural networks on time scales. Moreover, we give an example to illustrate the results obtained.

[1]  Yuanfu Shao,et al.  Analysis of stability for impulsive fuzzy Cohen–Grossberg BAM neural networks with delays , 2013 .

[2]  Ta-lun Yang,et al.  The global stability of fuzzy cellular neural network , 1996 .

[3]  Yeol Je Cho,et al.  Topological Degree Theory and Applications , 2006 .

[4]  Stephen Grossberg,et al.  Absolute stability of global pattern formation and parallel memory storage by competitive neural networks , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[5]  Wang,et al.  Qualitative analysis of Cohen-Grossberg neural networks with multiple delays. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Chuanzhi Bai,et al.  Stability analysis of Cohen–Grossberg BAM neural networks with delays and impulses , 2008 .

[7]  Tingwen Huang.  Exponential stability of fuzzy cellular neural networks with distributed delay , 2006 .

[8]  Jinde Cao,et al.  Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays , 2006 .

[9]  Lihong Huang,et al.  Anti-periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays☆ , 2009 .

[10]  A. Peterson,et al.  Dynamic Equations on Time Scales , 2001 .

[11]  Tianping Chen,et al.  Delay-independent stability analysis of Cohen-Grossberg neural networks , 2003 .

[12]  Jianying Shao,et al.  An anti-periodic solution for a class of recurrent neural networks , 2009 .

[13]  Yongkun Li,et al.  Global Exponential Stability and Existence of Periodic Solution of Impulsive Cohen–Grossberg Neural Networks with Distributed Delays on Time Scales , 2011, Neural Processing Letters.

[14]  S. Arik,et al.  Global stability analysis of Cohen–Grossberg neural networks with time varying delays , 2005 .

[15]  Qianhong Zhang,et al.  Global asymptotic stability of fuzzy cellular neural networks with time-varying delays , 2008 .

[16]  Tianping Chen,et al.  New Conditions on Global Stability of Cohen-Grossberg Neural Networks , 2003, Neural Computation.

[17]  Lili Wang,et al.  Existence and Stability of Anti-periodic Solutions for an Impulsive Cohen-Grossberg SICNNs on Time Scales , 2010 .

[18]  Leon O. Chua,et al.  Fuzzy cellular neural networks: applications , 1996, 1996 Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings (CNNA-96).

[19]  X. Zou,et al.  Harmless delays in Cohen–Grossberg neural networks ☆ , 2002 .

[20]  Q. Song,et al.  Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays , 2008 .

[21]  M. Bohner,et al.  Periodic solutions of functional dynamic equations with infinite delay , 2008 .

[22]  Jinde Cao,et al.  Stability in delayed Cohen–Grossberg neural networks: LMI optimization approach , 2005 .

[23]  Jinde Cao,et al.  Global output convergence of recurrent neural networks with distributed delays , 2007 .

[24]  G. Guseinov.  Integration on time scales , 2003 .

[25]  Zidong Wang,et al.  Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays , 2008 .

[26]  Wentao Wang,et al.  Anti-periodic solutions for a class of nonlinear nth-order differential equations with delays , 2009 .

[27]  Tingwen Huang.  Exponential stability of delayed fuzzy cellular neural networks with diffusion , 2007 .

[28]  Jinde Cao,et al.  An analysis of global asymptotic stability of delayed Cohen-Grossberg neural networks via nonsmooth analysis , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[29]  A. Peterson,et al.  Dynamic Equations on Time Scales: An Introduction with Applications , 2001 .

[30]  Jinde Cao,et al.  Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays , 2006, Neurocomputing.

[31]  Li Yang,et al.  Anti-periodic solutions for Cohen-Grossberg neural networks with bounded and unbounded delays , 2009 .

[32]  Yongkun Li.  Existence and stability of periodic solutions for Cohen–Grossberg neural networks with multiple delays , 2004 .

[33]  J. Ruan,et al.  Global dynamic analysis of general Cohen–Grossberg neural networks with impulse , 2007 .

[34]  A. Peterson,et al.  Advances in Dynamic Equations on Time Scales , 2012 .

[35]  Leon O. Chua,et al.  Fuzzy cellular neural networks: theory , 1996, 1996 Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings (CNNA-96).

[36]  Jianying Shao,et al.  Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays☆ , 2008 .

[37]  Qianhong Zhang,et al.  Existence and stability of anti-periodic solutions for impulsive fuzzy Cohen-Grossberge neural networks on time scales , 2014 .

[38]  Martin Bohner,et al.  Existence of Periodic Solutions in Predator Prey and Competition Dynamic Systems , 2006 .

[39]  Jinde Cao,et al.  Boundedness and stability for Cohen–Grossberg neural network with time-varying delays☆ , 2004 .

[40]  Youssef N. Raffoul,et al.  Periodic solutions for a neutral nonlinear dynamical equation on a time scale , 2006 .

[41]  Lu Zhao,et al.  Stability and existence of periodic solutions to delayed Cohen-Grossberg BAM neural networks with impulses on time scales , 2009, Neurocomputing.