Unfolding a codimension-two, discontinuous, Andronov-Hopf bifurcation

Chaos

Volumn 18, Issue 3, 2008, Pages

  Simpson, D J W ^a   Meiss, J D ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 54749100430     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2976165     Document Type: Article

References (22)

1. R. I. Leine and H. Nijmeijer, Dynamics and Bifurcations of Non-smooth Mechanical Systems, in Lecture Notes in Applied and Computational Mathematics Vol. 18 (Springer, Berlin, 2004).
2. Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities, edited by, M. Wiercigroch, and, B. De Kraker, (World Scientific, Singapore, 2000).
3. Nonlinear Phenomena in Power Electronics, edited by, S. Banerjee, and, G. C. Verghese, (IEEE, New York, 2001).
4. Z. T. Zhusubaliyev and E. Mosekilde, Bifurcations and Chaos in Piecewise-Smooth Dynamical Systems (World Scientific, Singapore, 2003).
5. C. K. Tse, Complex Behavior of Switching Power Converters (CRC, Boca Raton, 2003).
6. R. Rosen, Dynamical System Theory in Biology (Wiley-Interscience, New York, 1970).
7. J. Keener and J. Sneyd, Mathematical Physiology (Springer, New York, 1998).
8. M. di Bernardo, C. J. Budd, A. R. Champneys, and P. Kowalczyk, Piecewise-smooth Dynamical Systems. Theory and Applications (Springer, New York, 2008).
9. E. Freire, E. Ponce, and F. Torres, Publicacions Matemátiques 41, 131 (1997).
10. D. J. W. Simpson and J. D. Meiss, Phys. Lett. A 371, 213 (2007).
11. E. Freire, E. Ponce, F. Rodrigo, and F. Torres, Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, 2073 (1998).
12. V. Carmona, E. Freire, E. Ponce, and F. Torres, Int. J. Bifurcation Chaos Appl. Sci. Eng. 15, 2469 (2005).
13. Z. T. Zhusubaliyev and E. Mosekilde, Physica D 237, 930 (2008).
14. Z. T. Zhusubaliyev and E. Mosekilde, Phys. Lett. A 372, 2237 (2008).
15. D. J. W. Simpson, D. K. Kompala, and J. D. Meiss, " Discontinuity induced bifurcations in a model of Saccharomyces cerevisiae.," Math. Biosci. (submitted).
16. M. di Bernardo, C. J. Budd, and A. R. Champneys, Physica D 160, 222 (2001).
17. V. Carmona, E. Freire, E. Ponce, and F. Torres, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 49, 609 (2002).
18. H. Dankowicz and A. B. Nordmark, Physica D 136, 280 (2000).
19. J. Guckenheimer and P. J. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, New York, 1986).
20. Yu. A. Kuznetsov, Elements of Bifurcation Theory, in Appl. Math. Sci. Vol. 112 (Springer, New York, 2004).
21. P. Glendinning, Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations (Cambridge University Press, New York, 1999).
22. D. J. W. Simpson, Ph.D. thesis, University of Colorado, in progress.