|
|
Chaos from Orbit-Flip Homoclinic Orbits Generated in a Practical Circuit
Hisa-Aki Tanaka
Physical Review Letters, 1995.
Abstract
A new class of chaotic systems is generated in a practical, nonlinear, mutually coupled phase-locked loop (PLL) circuit.
Theoretical results make it possible to understand experimental results of such PLL's on the onset of chaos using the geometry of the invariant manifolds,
while the resultant simple geometry and complex dynamics is expected to have applications in other areas,
e.g., power systems or interacting bar magnets.
The 1D map projected from a numerically obtained attractor indicates the existence of a piece-wise linear structure having a sensitive dependence on the bifurcation parameter f02.
Download PDF
Figures at a glance
References
- L. P. Shil'nikov, Sov. Math Dokl. 6, 163 (1965).
- J. W. Evans, N. Fenichel, and J. A. Feroe, SIAM J. Appl. Math. 42, 219 (1982).
- E. Yanagida, J. Diff. Eq. 66, 243 (1987).
- H. Kokubu and H. Oka (to be published).
- A. J. Homburg, H. Kokubu, and M. Krupa (to be published).
- K. Iori, E. Yanagida, and T. Matsumoto, in Structure and Bifurcations of Dynamical Systems,S. Ushiki, Advanced Series in Dynamical Systems Vol. 11 (World Scientific, Singapore, 1993), p. 82.
- T. Endo and L. O. Chua, IEEE Trans., CAS Vol. 37, No. 9, 1183 (1990).
- M. Kisaka, H. Kokubu, and H. Oka, J. Dynam. Diff. Eq. 5, 305 (1993).
- F. M. A. Salam, J. E. Marsden, and P. P. Varaiya, IEEE Trans., CAS, Vol. 31, No. 8, 673 (1984).
- S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Massachusetts, 1994), p. 286.
|
|
 |
