Bi-periodicity evoked by periodic external inputs in delayed Cohen–Grossberg-type bidirectional associative memory networks

In this paper, the bi-periodicity issue is discussed for Cohen?Grossberg?type (CG-type) bidirectional associative memory (BAM) neural networks (NNs) with time-varying delays and standard activation functions. It is shown that the model considered in this paper has two periodic orbits located in saturation regions and they are locally exponentially stable. Meanwhile, some conditions are derived to ensure that, in any designated region, the model has a locally exponentially stable or globally exponentially attractive periodic orbit located in it. As a special case of bi-periodicity, some results are also presented for the system with constant external inputs. Finally, four examples are given to illustrate the effectiveness of the obtained results.

[1]  Jiye Zhang,et al.  Global exponential stability of Cohen–Grossberg neural networks with variable delays☆ , 2005 .

[2]  Lin Wang,et al.  Capacity of stable periodic solutions in discrete-time bidirectional associative memory neural networks , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

[4]  Richard H. R. Hahnloser,et al.  On the piecewise analysis of networks of linear threshold neurons , 1998, Neural Networks.

[5]  Yang Shuzi,et al.  Stability of general neural networks with reaction-diffusion , 2001 .

[6]  CHIH-WEN SHIH,et al.  Multistability in Recurrent Neural Networks , 2006, SIAM J. Appl. Math..

[7]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[8]  Jinde Cao,et al.  Stability in Cohen–Grossberg-type bidirectional associative memory neural networks with time-varying delays , 2006 .

[9]  Zhigang Zeng,et al.  Memory pattern analysis of cellular neural networks , 2005 .

[10]  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.

[11]  K. Gopalsamy,et al.  Global asymptotic stability in a periodic Lotka-Volterra system , 1985, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[12]  David H. Owens,et al.  Existence and learning of oscillations in recurrent neural networks , 2000, IEEE Trans. Neural Networks Learn. Syst..

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

[14]  Xue-Zhong He,et al.  Delay-independent stability in bidirectional associative memory networks , 1994, IEEE Trans. Neural Networks.

[15]  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.

[16]  Foss,et al.  Multistability and delayed recurrent loops. , 1996, Physical review letters.

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

[18]  T. Liao,et al.  Globally exponential stability of generalized Cohen–Grossberg neural networks with delays , 2003 .

[19]  Masahiko Morita,et al.  Associative memory with nonmonotone dynamics , 1993, Neural Networks.

[20]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Jinde Cao,et al.  Exponential stability and periodic oscillatory solution in BAM networks with delays , 2002, IEEE Trans. Neural Networks.

[22]  Lihong Huang,et al.  Global existence of periodic solutions of BAM neural networks with variable coefficients , 2003 .

[23]  Jun Wang,et al.  Multiperiodicity and Exponential Attractivity Evoked by Periodic External Inputs in Delayed Cellular Neural Networks , 2006 .

[24]  Jinde Cao,et al.  Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays , 2004 .

[25]  DeLiang Wang,et al.  Weight adaptation and oscillatory correlation for image segmentation , 2000, IEEE Trans. Neural Networks Learn. Syst..

[26]  V. Sree Hari Rao,et al.  Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zones , 1999, Neural Networks.

[27]  Sabri Arik,et al.  Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays , 2005, IEEE Transactions on Neural Networks.

[28]  E. I. El-Masry,et al.  A switched capacitor bidirectional associative memory , 1990 .

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

[30]  Miriam Zacksenhouse,et al.  Oscillatory neural networks for robotic yo-yo control , 2003, IEEE Trans. Neural Networks.

[31]  Chang-Yuan Cheng,et al.  Multistability and convergence in delayed neural networks , 2007 .

[32]  Lin Wang,et al.  Exponential stability of Cohen-Grossberg neural networks , 2002, Neural Networks.

[33]  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.

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