On Period-adding Sequences of Attracting Cycles in Piecewise Linear Maps

Chaos, Solitons and Fractals

Volumn 9, Issue 1-2, 1998, Pages 67-75

  Maistrenko, Yu L ^a   Maistrenko, V L ^a   Vikul, S I ^a  

^a INSTITUTE OF MATHEMATICS   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; FUNCTIONS; MATHEMATICAL TECHNIQUES; NUMERICAL METHODS;

ATTRACTING CYCLES; PIECEWISE LINEAR MAPS;

BIFURCATION (MATHEMATICS);

EID: 0031673927     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(97)00049-0     Document Type: Article

References (12)

1. Maistrenko, Yu. L., Maistrenko, V. L., Vikul, S. I. and Chua, L. O., Bifurcation of attracting cycles from time-delayed Chua's circuit. Int. J. Bifurcation and Chaos, 1995, 5(3), 653-671.
2. Maistrenko, Yu. L., Maistrenko, V. L. and Vikul, S. T., Bifurcation of attracting cycles of piecewise linear interval maps. J. Tech., Phys., 1996, 37(3-4), 367-370.
3. Maistrenko, Yu. L., Maistrenko, V. L. and Vikul, S. I., Transition from unimodal to bimodal maps in one-dimensional piecewise linear models. In Proc. Int. Conf. ICNBC'96, Poland, 16-18 September, 1996, pp. 173-179.
4. Gumowski, I. and Mira, Ch., Dynamique Chaotique. Cepadues Editions, Toulouse, 1980.
5. Mira, Ch., Gardini, L., Barugola, A. and Cathala, J. C., Chaotic Dynamics in Two-dimensional Noninvertible Maps, Series A, Vol. 20. World Scientific, Singapore, 1996.
6. Maistrenko, V. L., Maistrenko, Yu. L. and Sushko, I. M., Attractors of piecewise linear maps of straight line and plane. Preprint #92.33 Inst. Math. Ukr. Acad. Sci., 1992. In Russian.
7. Maistrenko, Yu. L., Maistrenko, V. L. and Chua, L. O., Cycles of chaotic intervals in a time-delayed Chua's circuits. Int. J. Bifurcation and Chaos, 1993, 3(6), 1557-1572.
8. Veitch, D. and Glendinning, P., Explicit renormalization in piecewise linear bimodal maps. Physica D, 1990, 44, 149-167.
9. Nusse, H. E. and Yorke, J. A., Border-collision bifurcations for piecewise smooth one-dimensional maps. Int. J. Bifurcation and Chaos, 1995, 5(1), 189-207.
10. de Melo, W. and van Strien, S., One-Dimensional Dynamics. Springer-Verlag, Berlin, Chap. 1, pp. 14-80.
11. Leonov, N. N., Map on the line on to itself. Radiophysics, 1959, 2(6), 942-956. In Russian.
12. Mira, Ch., Chaotic Dynamics. World Scientific, Singapore, 1987.