Equilibrium Analysis for Improved Signal Range Model of Delayed Cellular Neural Networks

In this paper, a class of delayed cellular neural networks with unbounded activation functions and described by using space invariant cloning templates are considered. The general and explicit existing regions of equilibrium points are discussed based on dissipative theory, fixed point principle of iteration mapping and Brouwer Fixed-point Theorem. The sufficient condition is obtained to ensure the existence, uniqueness, local asymptotical stability of the equilibrium point in each saturation sub-region. Moreover, we give the condition for equilibrium point to be globally exponentially stable, and the explicit existing region of the unique equilibrium point is also located. These results extend previous works on these issues for the standard delayed cellular neural networks. Two numerical examples are given to show the validity of the obtained results.

[1]  Cheng-Hsiung Hsu.  Smale Horseshoe of Cellular Neural Networks , 2000, Int. J. Bifurc. Chaos.

[2]  Jun Wang,et al.  Global dissipativity of continuous-time recurrent neural networks with time delay. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Cheng-Hsiung Hsu,et al.  Spatial disorder of Cellular Neural Networks , 2002 .

[4]  Leon O. Chua,et al.  Cellular neural networks: applications , 1988 .

[5]  Jinde Cao.  A set of stability criteria for delayed cellular neural networks , 2001 .

[6]  Zhigang Zeng,et al.  Positive invariant and global exponential attractive sets of neural networks with time-varying delays , 2008, Neurocomputing.

[7]  S. Arik,et al.  Equilibrium analysis of delayed CNNs , 1998 .

[8]  Yan Huang,et al.  Horseshoe and topological entropy estimate of a class of three-dimensional cellular neural networks , 2008, Appl. Math. Comput..

[9]  Á. Rodríguez-Vázquez,et al.  Current-mode techniques for the implementation of continuous- and discrete-time cellular neural networks , 1993 .

[10]  L. Chua,et al.  A more rigorous proof of complete stability of cellular neural networks , 1997 .

[11]  Jun Wang,et al.  Global exponential stability of a general class of recurrent neural networks with time-varying delays , 2003 .

[12]  Zhigang Zeng,et al.  Stability analysis of delayed cellular neural networks described using cloning templates , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..

[13]  Leon O. Chua,et al.  Stability of cellular neural networks with dominant nonlinear and delay-type templates. (Memo UCB/ERL No. M92/121.) , 1993 .

[14]  Leon O. Chua,et al.  On the universe of stable cellular neural networks , 1992, Int. J. Circuit Theory Appl..

[15]  P. Kaluzny.  Number of stable equilibrium states of cellular neural networks , 1994 .

[16]  Cheng-Hsiung Hsu,et al.  Spatial Disorder of Cellular Neural Networks - with Biased Term , 2002, Int. J. Bifurc. Chaos.

[17]  Ricardo Carmona-Galán,et al.  A VLSI-oriented continuous-time CNN model , 1996, Int. J. Circuit Theory Appl..

[18]  Vedat Tavsanoglu,et al.  An equilibrium analysis of CNNs , 1998 .

[19]  Leon O. Chua,et al.  The CNN paradigm , 1993 .

[20]  Leon O. Chua,et al.  Cellular neural networks with non-linear and delay-type template elements and non-uniform grids , 1992, Int. J. Circuit Theory Appl..

[21]  Jinde Cao,et al.  Global asymptotic stability of a general class of recurrent neural networks with time-varying delays , 2003 .

[22]  Duccio Papini,et al.  Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain , 2005, IEEE Transactions on Neural Networks.

[23]  Marco Gilli,et al.  Equilibrium analysis of cellular neural networks , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Cheng-Hsiung Hsu,et al.  Spatial disorder of CNN - with Asymmetric output Function , 2001, Int. J. Bifurc. Chaos.

[25]  M. Forti,et al.  Global convergence of neural networks with discontinuous neuron activations , 2003 .

[26]  Fang-Yue Chen,et al.  Chaotic Stationary Solutions of Cellular Neural Networks , 2003, Int. J. Bifurc. Chaos.

[27]  Tamás Roska,et al.  Cellular neural networks with nonlinear and delay-type template elements , 1990, IEEE International Workshop on Cellular Neural Networks and their Applications.

[28]  Leon O. Chua,et al.  The analogic cellular neural network as a bionic eye , 1995, Int. J. Circuit Theory Appl..

[29]  Qiang Zhang,et al.  An analysis on the global asymptotic stability for neural networks with variable delays , 2004 .