On the prediction of period-doubling bifurcations in almost reciprocal cellular neural networks

The Harmonic Balance (HB) method is exploited for addressing the possible existence of period-doubling bifurcations, and complex dynamics, in a class of almost symmetric Cellular Neural Networks (CNNs). In particular, sets of CNNs parameters close to symmetry, for which period-doubling bifurcations are predicted by the HB method, are singled out. The reliability and accuracy of these predictions are shown by means of computer simulations.

[1]  A. Michel,et al.  Robustness and Perturbation Analysis of a Class of Nonlinear Systems with Applications to Neural Networks , 1993, 1993 American Control Conference.

[2]  Mathukumalli Vidyasagar.  Minimum-seeking properties of analog neural networks with multilinear objective functions , 1995, IEEE Trans. Autom. Control..

[3]  Shlomo Engelberg,et al.  Limitations of the describing function for limit cycle prediction , 2002, IEEE Trans. Autom. Control..

[4]  G. Siouris,et al.  Nonlinear Control Engineering , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[5]  Marco Gilli,et al.  Analysis of stability and bifurcations of limit cycles in Chua's circuit through the harmonic-balance approach , 1999 .

[6]  A. I. Mees,et al.  Dynamics of feedback systems , 1981 .

[7]  M. DI MARCO,et al.  Bifurcations and oscillatory Behavior in a Class of Competitive Cellular Neural Networks , 2000, Int. J. Bifurc. Chaos.

[8]  Leon O. Chua,et al.  A CNN chip for connected component detection , 1991 .

[9]  Alberto Tesi,et al.  Harmonic Balance Approach To Predict Period-Doubling Bifurcations In Nearly Symmetric CNNs , 2003, J. Circuits Syst. Comput..

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

[11]  Alberto Tesi,et al.  A Frequency Method for Predicting Limit Cycle Bifurcations , 1997 .

[12]  Leon O. Chua,et al.  CNN: A Vision of Complexity , 1997 .

[13]  L.O. Chua,et al.  Cellular neural networks , 1993, 1988., IEEE International Symposium on Circuits and Systems.

[14]  M. Gilli,et al.  An approximate analytical approach for predicting period-doubling in the Colpitts oscillator , 1998, ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187).

[15]  A. Tesi,et al.  Existence and characterization of limit cycles in nearly symmetric neural networks , 2002 .