Complex behavior in digital filters with overflow nonlinearity: analytical results

IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing

Volumn 43, Issue 3, 1996, Pages 234-246

  Kocarev, Ljupco ^a,b   Wu, Chai Wall ^a,c   Chua, Leon O ^a,c  

^a IEEE

^b SS CYRIL AND METHODIUS UNIVERSITY   (Macedonia)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; DISCRETE TIME CONTROL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; FRACTALS; LYAPUNOV METHODS; MATHEMATICAL MODELS; THEOREM PROVING;

BERNOULLI SYSTEM; HAUSDORFF DIMENSION; HYPERBOLIC ATTRACTOR; INTEGERS; LYAPUNOV EXPONENT; OVERFLOW NONLINEARITY;

DIGITAL FILTERS;

EID: 0030107402     PISSN: 10577130     EISSN: None     Source Type: Journal    
DOI: 10.1109/82.486469     Document Type: Article

References (15)

1. P. M. Ebert. J. E. Mazo, and M. G. Taylor, "Overflow oscillations in digital filters," Bell Sysr. Tech.J. vol. 48, pp. 2999-3020, Nov. 1969.
2. L. O. Chua and T. Lin, "Chaos in digital filters," IEEE Trans. Circuits Syst., vol. 35, pp. 648-658, June 1988.
3. R. Boite and X.-Q. Yang, "On the free overflow oscillations in digital filters," Tech. Rep., 1989, (preprint).
4. L. O. Chua and T. Lin, "Fractal pattern of second-order nonlinear digital filters: A new symbolic analysis," Int. J. Circuit Theory Applicat., vol. 18, pp. 541-550, 1990.
5. M. J. Ogorzalek, "Complex behavior in digital filters," Int. J. Bifurc. Chaos, vol. 2, no. 1, pp. 11-29, 1992.
6. Z. Galias and M. Ogorzalek, "On symbolic dynamics of a chaotic second-order digital filter," Int. J. Circuit Theory Applicat., vol. 20, no. 4, pp. 401-409, 1992.
7. C. W. Wu and L. O. Chua, "Properties of admissible symbolic sequences in a second order digital (liter with overflow nonlinearity," Int. J. Circuit Theory Applicat., vol. 21, no. 3, pp. 299-307, 1993.
8. L. Kocarev and L. O. Chua, "On chaos in digital filters: Case b= -1," IEEE Trans. Circuits Syst. -II, vol. 40, pp. 404-407, June 1993.
9. V. I. Arnold and A. Avez, Ergodic: Problems of Ctassicfil Mechanics. Mathematical Physics Monograph Series. New York: Benjamin, 1968.
10. R. Finn and L. J. Lara, "On the .symmetry lines of the standard mapping," Physica. vol. 26D, pp. 369-378, 1987.
11. V. N. Belykh, "Models of discrets systems of phase synchronization," Radio and Communication. Moscow, 1982, (in Russian) ch. 10, pp. 161-176.
12. Y. G. Sinai, Ed., Dynamical Systems, vol. 2 of Encyclopedia of Mathematical Sciences. New York: Springer-Verlag, 1989.
13. Y. Pesin, "Ergodic properties and dimensionlike characteristics of strange attractors thaï are close to hyperbolic," in Proc. Int. Congress of Mathemal., 1986, pp. 1195-1209.
14. V. N. Belykh and I. L. Zelezniak, "Dimension estimation of a strange attractor in a two-dimensional discontinous map," Tech. Rep., 1991, preprint (in Russian).
15. A. Lasota and M. C. Mackey, Probabilistic Properties of Determinism: Systems. Cambridge: Cambridge University Press, 1985.