TY - JOUR
T1 - Chaos from orbit-flip homoclinic orbits generated in real systems
AU - Tanaka, Hisa Aki
AU - Oishi, Shin'ichi
AU - Horiuchi, Kazuo
PY - 1995/1/1
Y1 - 1995/1/1
N2 - A new class of chaotic systems is discovered that are generated in a practical, nonlinear, mutually coupled phase-locked loop (PLL) circuit. Presented theoretical results make it possible to understand experimental results of mutually coupled 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. Motivated by the numerical study of this system, the topological horseshoe is proven to be generated in the codimension 3 unfolding of a degenerated orbit-flip homoclinic point for this system. Qualitatively different type of bifurcation phenomena are also observed to appear depending on the phase detector (PD) characteristics.
AB - A new class of chaotic systems is discovered that are generated in a practical, nonlinear, mutually coupled phase-locked loop (PLL) circuit. Presented theoretical results make it possible to understand experimental results of mutually coupled 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. Motivated by the numerical study of this system, the topological horseshoe is proven to be generated in the codimension 3 unfolding of a degenerated orbit-flip homoclinic point for this system. Qualitatively different type of bifurcation phenomena are also observed to appear depending on the phase detector (PD) characteristics.
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M3 - Conference article
AN - SCOPUS:0029192745
VL - 1
SP - 263
EP - 266
JO - Proceedings - IEEE International Symposium on Circuits and Systems
JF - Proceedings - IEEE International Symposium on Circuits and Systems
SN - 0271-4310
T2 - Proceedings of the 1995 IEEE International Symposium on Circuits and Systems-ISCAS 95. Part 3 (of 3)
Y2 - 30 April 1995 through 3 May 1995
ER -