Harmonic balance approach to predict period-doubling bifurcations in nearly symmetric CNNs

Journal of Circuits, Systems and Computers

Volumn 12, Issue 4, 2003, Pages 435-459

  Di Marco, Mauro ^a   Forti, Mauro ^a   Tesi, Alberto ^b  

^a UNIVERSITY OF SIENA   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Cellular neural networks; Complete stability; Harmonic balance; Period doubling bifurcations; Robustness

Indexed keywords

BIFURCATION (MATHEMATICS); CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; HARMONIC ANALYSIS; LARGE SCALE SYSTEMS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; ROBUSTNESS (CONTROL SYSTEMS);

HARMONIC BALANCE; NEURON INTERCONNECTIONS;

CELLULAR NEURAL NETWORKS;

EID: 0346907095     PISSN: 02181266     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218126603000969     Document Type: Article

References (20)

1. L. O. Chua and L. Yang, "Cellular neural networks: Theory", IEEE Trans. Circuits Syst. 35 (1988) 1257-1272.
2. L. O. Chua, "CNN: A vision of complexity", Int. J. Bifur. Chaos 7 (1997) 2219-2425.
3. M. Vidyasagar, "Minimum-seeking properties of analog neural networks with multi-linear objective functions", IEEE Trans. Automatic Control 40 (1995) 1359-1375.
4. K. Wang and A. N. Michel, "Robustness and perturbation analysis of a class of nonlinear systems with applications to neural networks", IEEE Trans. Circuits Syst.I 41 (1994) 24-32.
5. J. M. Cruz and L. O. Chua, "A CNN chip for connected component detection", IEEE Trans. Circuits Syst. 38 (1991) 812-817.
6. M. Di Marco, M. Forti, and A. Tesi, "Bifurcations and oscillatory behavior in a class of competitive cellular neural networks", Int. J. Bifur. Chaos 10 (2000) 1267-1293.
7. M. Di Marco, M. Forti, and A. Tesi, "Existence and characterization of limit cycles in nearly symmetric neural networks", IEEE Trans. Circuits Syst. I 49 (2002) 979-992.
8. M. Di Marco, M. Forti, and A. Tesi, "Complex dynamics in nearly-symmetric three-cell cellular neural networks", Int. J. Bifur. Chaos 12 (2002) 1357-1362.
9. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1983.
10. S. Wiggins, Global Bifurcations and Chaos: Analytical Methods, Springer-Verlag, New York, 1988.
11. R. Genesio and A. Tesi, "A harmonic balance approach for chaos prediction: Chua's circuit", Int. J. Bifur. Chaos 2 (1992) 61-79.
12. A. Tesi, E. H. Abed, R. Genesio, and H. O. Wang, "Harmonic balance analysis of period-doubling bifurcations with implications for control of nonlinear dynamics", Automatica 32 (1996) 1255-1271.
13. M. Basso, R. Genesio, and A. Tesi, "A frequency method for predicting limit cycle bifurcations", Nonlinear Dynamics 13 (1997) 339-360.
14. F. Bonani and M. Gilli, "Analysis of stability and bifurcations of limit cycles in Chua's circuit through the harmonic-balance approach", IEEE Trans. Circuits Syst. I 46 (1999) 881-890.
15. M. Forti and A. Tesi, "A new method to analyze complete stability of PWL cellular neural networks", Int. J. Bifur. Chaos 11 (2001) 655-676.
16. D. Atherton, Nonlinear Control Engineering, Van Nostrand Reinhold, London, 1975.
17. A. Mees, Dynamics of Feedback Systems, Wiley, New York, 1981.
18. M. Vidyasagar, Nonlinear System Analysis, Prentice Hall, Englewood Cliffs, NJ, 1993.
19. G. Iooss and D. Joseph, Elementary Stability and Bifurcation Theory, Springer-Verlag, New York, 2nd edition, 1989.
20. L. O. Chua and G.-N. Lin, "Canonical realization of Chua's circuit family", IEEE Trans. Circuits Syst. 37 (1990) 885-902.