Equilibrium-torus bifurcation in nonsmooth systems

Physica D: Nonlinear Phenomena

Volumn 237, Issue 7, 2008, Pages 930-936

  Zhusubaliyev, Zhanybai T ^a   Mosekilde, Erik ^b  

^a SOUTHWEST STATE UNIVERSITY   (Russian Federation)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

Border collision bifurcation; Equilibrium point; Nonsmooth systems; Two dimensional torus

Indexed keywords

APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); DIFFERENTIAL EQUATIONS; NUMERICAL METHODS; PARAMETER ESTIMATION;

DISCONTINUITY BOUNDARY; EQUILIBRIUM POINTS;

SYSTEMS ANALYSIS;

EID: 42249113497     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2007.11.019     Document Type: Article

References (27)

1. In: Banerjee S., and Verghese G.C. (Eds). Nonlinear Phenomena in Power Electronics (2001), IEEE Press, New York, USA
2. Tse C.K. Complex Behavior of Switching Power Converters (2003), CRC Press, Boca Raton, USA
3. Zhusubaliyev Zh.T., and Mosekilde E. Bifurcations and Chaos in Piecewise-Smooth Dynamical Systems (2003), World Scientific, Singapore
4. Brogliato B. Nonsmooth Mechanics - Models, Dynamics and Control (1999), Springer Verlag, New York
5. Nordmark A.B. Non-periodic motion caused by grazing incidence in an impact oscillator. J. Sound Vibration 145 2 (1991) 279-297
6. Garcia M., Chatterjee A., Ruina A., and Coleman M. The simplest walking model: Stability, complexity, and scaling. ASME J. Biomechan. Eng. 120 2 (1998) 281-288
7. Keener J., and Sneyd J. Mathematical Physiology (1998), Springer Verlag, New York
8. Laugesen J., and Mosekilde E. Border-collision bifurcations in a dynamic management game. Comput. Oper. Res. 33 (2006) 464-478
9. Feigin M.I. Doubling of the oscillation period with C-bifurcations in piecewise continuous systems. Prikl. Mat. Mekh. 34 5 (1970) 861-869 (in Russian)
10. Feigin M.I. Forced Oscillations in Systems with Discontinuous Nonlinearities (1994), Nauka Publ., Moscow (in Russian)
11. Nusse H.E., and Yorke J.A. Border-collision bifurcations including period two to period three for piecewise smooth systems. Physica D 57 (1992) 39-57
12. Nusse H.E., Ott E., and Yorke J.A. Border-collision bifurcations: An explanation for observed bifurcation phenomena. Phys. Rev. E 49 (1994) 1073-1076
13. Nusse H.E., and Yorke J.A. Border-collision bifurcation for piecewise smooth one-dimensional maps. Internat. J. Bifur. Chaos 5 1 (1995) 189-207
14. di Bernardo M., Feigin M.I., Hogan S.J., and Homer M.E. Local analysis of C-bifurcations in n-dimensional piecewise-smooth dynamical systems. Chaos, Solitons and Fractals 10 11 (1999) 1881-1908
15. Dutta M., Nusse H.E., Ott E., Yorke J.A., and Yuan G.-H. Multiple attractor bifurcations: A source of unpredictability in piecewise smooth systems. Phys. Rev. Lett. 83 (1999) 4281-4284
16. Kapitaniak T., and Maistrenko Yu.L. Multiple choice bifurcations as a source of unpredictability in dynamical systems. Phys. Rev. E 58 4 (1998) 5161-5163
17. Banerjee S., Yorke J.A., and Grebogi C. Robust chaos. Phys. Rev. Lett. 80 14 (1998) 3049-3052
18. di Bernardo M., Budd C.J., and Champneys A.R. Corner collision implies border collision. Physica D 154 3-4 (2001) 171-194
19. di Bernardo M., Budd C.J., and Champneys A.R. Grazing and border-collision in piecewise-smooth systems: A unified analytical framework. Phys. Rev. Lett. 86 12 (2001) 2553-2556
20. di Bernardo M., Kowalczyk P., and Nordmark A. Bifurcations of dynamical systems with sliding: Derivation of normal-form mappings. Physica D 170 (2002) 175-205
21. Kowalczyk P., Bernardo d., Champneys A.R., Hogan S.J., Homer M., Kuznetsov Yu.A., and Nordmark A.B. Two-parameter discontinuity-induced bifurcations of limit cycles: Classification and open problems. Internat. J. Bifur. Chaos 16 3 (2006) 601-629
22. Zhusubaliyev Zh.T., and Mosekilde E. Torus birth bifurcation in a DC/DC converter. IEEE Trans. Circ. Syst. I: Fund. Theory and Appl. 53 8 (2006) 1839-1850
23. Zhusubaliyev Zh.T., Mosekilde E., Maity S.M., Mohanan S., and Banerjee S. Border collision route to quasiperiodicity: Numerical investigation and experimental confirmation. Chaos 16 (2006) 023122
24. A.V. Kobzev, G.Ya Michal'chenko, N.M. Muzhitchenko, Modulating Power Supplies of Radioelectronic Devices, Radio i Svyaz, Tomsk, 1990 (in Russian)
25. Banerjee S., and Grebogi C. Border collision bifurcations in two-dimensional piecewise smooth maps. Phys. Rev. E 59 4 (1999) 4052-4061
26. Gelig A.K., and Churilov A.N. Stability and Oscillations of Nonlinear Pulse-Modulated Systems (1998), Birkhäuser, Boston
27. Avrutin V., and Schanz M. On multi-parametric bifurcations in a scalar piecewise-linear map. Nonlinearity 19 3 (2006) 531-552