Bifurcation analysis in a discrete BAM network model with delaysFootnote

^†This research is supported by the National Natural Science Foundation of China (No.10771045) and Program of Excellent Team in Harbin Institute of Technology.

References

• Babcock , K.L. and Westervelt , R.M. 1987 . Dynamics of simple electronic neural networks . Phys. D , 28 : 305 – 316 .
   Web of Science ®Google Scholar
• Baldi , P. and Atiya , A. 1994 . How delays affect neural dynamics and learning . IEEE Trans. Neural Netw. , 5 : 610 – 621 .
   Google Scholar
• Cushing , J.M. and Henson , S.M. 2001 . Global dynamics of some periodically forced monotone difference equations . J. Differ. Equ. Appl. , 7 : 859 – 872 .
   Web of Science ®Google Scholar
• Elaydi , S. 2005 . An Introduction to Difference Equations , 3rd ed. , New York : Springer .
   Google Scholar
• Fan , D. and Wei , J. 2008 . Hopf bifurcation analysis in a tri-neuron network with time delay . Nonlinear Anal. Real World Appl. , 9 : 9 – 25 .
   Web of Science ®Google Scholar
• Faria , T. 2000 . On a planar system modelling a neuron network with memory . J. Differ. Equ. , 168 : 129 – 149 .
   Google Scholar
• Gopalsamy , K. and He , X. 1994 . Delay-independent stability in bi-directional associative memory networks . IEEE Trans. Neural Netw. , 5 : 998 – 1002 .
   PubMed Web of Science ®Google Scholar
• Gopalsamy , K. and Leung , I. 1996 . Delay induced periodicity in a neural network of excitation and inhibition . Phys. D , 89 : 395 – 426 .
   Google Scholar
• Guo , S. and Huang , L. 2003 . Hopf bifurcating periodic orbits in a ring of neurons with delays . Pyhs. D , 183 : 19 – 44 .
   Web of Science ®Google Scholar
• Guo , S. , Tang , X. and Huang , L. 2008 . Stability and bifurcation in a discrete system of two neurons with delays . Nonlinear Anal. Real World Appl. , 9 : 1323 – 1335 .
   Google Scholar
• Hopfield , J.J. 1984 . Neurons with graded response have collective computational properties like those of two-state neurons . Proc. Natl Acad. Sci. USA , 81 : 3088 – 3092 .
   PubMed Web of Science ®Google Scholar
• Kuznetsov , Y.A. 1998 . Elements of Applied Bifurcation Theory , New York : Spring-Verlag .
   Google Scholar
• Kuznetsov , Y.A. and Meijer , H.G.E. 2006 . Remarks on interaction Neimark–Sacker bifurcations . J. Differ. Equ. Appl. , 12 ( 10 ) : 1009 – 1035 .
   Web of Science ®Google Scholar
• Mohamad , S. 2003 . Global exponential stability in discrete-time analogues of delayed cellular neural networks . J. Differ. Equ. Appl. , 9 ( 6 ) : 559 – 575 .
   Web of Science ®Google Scholar
• Mohamad , S. and Gopalsamy , K. 2000 . Dynamics of a class of discrete-time neural networks and their continuous-time counterparts . Math. Comput. Simul. , 53 : 1 – 39 .
   Google Scholar
• Mohamad , S. and Naim , A. 2002 . Discrete-time analogues of integrodifferential equations modelling bidirectional neural networks . J. Comput. Appl. Math. , 138 : 1 – 20 .
   Google Scholar
• Murakami , K. 2005 . Stability for non-hyperbolic fixed points of scalar difference equations . J. Differ. Equ. Appl. , 310 ( 2 ) : 492 – 505 .
   Google Scholar
• Song , Y. , Han , M. and Wei , J. 2005 . Stability and Hopf bifurcation on a simplified BAM neural network with delays . Phys. D , 200 : 185 – 204 .
   Google Scholar
• Stuart , A. and Humphries , A. 1996 . Dynamical Systems and Numerical Analysis , Cambridge : Cambridge University Press .
   Google Scholar
• Wang , C. and Wei , J. 2008 . Bifurcation analysis on a discrete model of Nicholson's blowflies . J. Differ. Equ. Appl. , 14 ( 7 ) : 737 – 746 .
   Web of Science ®Google Scholar
• Wang , L. and Zou , X. 2004 . Hopf bifurcation in bidirectional associative memory neural networks with delays: Analysis and computation . J. Comput. Appl. Math. , 167 : 73 – 90 .
   Google Scholar
• Wei , J. and Li , M.Y. 2004 . Global existence of periodic solutions in a tri-neuron network model with delays . Phys. D , 198 : 106 – 119 .
   Web of Science ®Google Scholar
• Wei , J. and Zhang , C. 2008 . Bifurcation analysis of a class of neural networks with delays . Nonlinear Anal. Real World Appl. , 9 : 2234 – 2252 .
   Web of Science ®Google Scholar
• Wu , J. 2001 . Introduction to Neural Dynamics and Signal Transmission Delay , Berlin, New York : Walter de Gruyter .
   Google Scholar
• Yan , X. 2008 . Bifurcation analysis in a simplified tri-neuron BAM network model with multiple delays . Nonlinear Anal. , 9 : 963 – 976 .
   Google Scholar
• Zheng , B. , Zhang , Y. and Zhang , C. 2008 . Stability and bifurcation of a discrete BAM neural network model with delays . Chaos Solitons Fractals , 36 : 612 – 616 .
   Web of Science ®Google Scholar