Homoclinic Orbits, Fractal Basin Boundaries and Bifurcations of Phase-Locked Loop Circuits

Tetsuro ENDO

Homoclinic Orbits, Fractal Basin Boundaries and Bifurcations of Phase-Locked Loop Circuits

Tetsuro ENDO

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The phase-locked loop (PLL) is a versatile functional device widely used in many electronic system. We found previously that the PLL can become chaotic under some operating conditions for wide range of system parameter values. The reason why the PLL can cause chaos is closely related to the homoclinic orbits of which existence are proved by Melnikov method. In this paper, we review the motivation and significance of chaos occurring in the PLL circuits. Then we confirm various chaotic characteristics of the phase-locked loop equation having the homoclinic orbits such as the fractal basin boundaries and sensitive dependence on initial conditions of a solution. At last, we investigate the route to chaos of the periodic solution of first type (PS1) by calculating the bifurcation diagram, and presents a new results that the PS1 can be chaotic via the period-doubling cascade.

Publication: IEICE TRANSACTIONS on transactions Vol.E73-E No.6 pp.828-835

Publication Date: 1990/06/25

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Type of Manuscript: Special Section PAPER (Special Issue on Engineering Chaos)

Category: Chaos in Electrical Circuits

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Tetsuro ENDO

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Tetsuro ENDO, "Homoclinic Orbits, Fractal Basin Boundaries and Bifurcations of Phase-Locked Loop Circuits" in IEICE TRANSACTIONS on transactions, vol. E73-E, no. 6, pp. 828-835, June 1990, doi: .
Abstract: The phase-locked loop (PLL) is a versatile functional device widely used in many electronic system. We found previously that the PLL can become chaotic under some operating conditions for wide range of system parameter values. The reason why the PLL can cause chaos is closely related to the homoclinic orbits of which existence are proved by Melnikov method. In this paper, we review the motivation and significance of chaos occurring in the PLL circuits. Then we confirm various chaotic characteristics of the phase-locked loop equation having the homoclinic orbits such as the fractal basin boundaries and sensitive dependence on initial conditions of a solution. At last, we investigate the route to chaos of the periodic solution of first type (PS1) by calculating the bifurcation diagram, and presents a new results that the PS1 can be chaotic via the period-doubling cascade.
URL: https://globals.ieice.org/en_transactions/transactions/10.1587/e73-e_6_828/_p

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@ARTICLE{e73-e_6_828,
author={Tetsuro ENDO, },
journal={IEICE TRANSACTIONS on transactions},
title={Homoclinic Orbits, Fractal Basin Boundaries and Bifurcations of Phase-Locked Loop Circuits},
year={1990},
volume={E73-E},
number={6},
pages={828-835},
abstract={The phase-locked loop (PLL) is a versatile functional device widely used in many electronic system. We found previously that the PLL can become chaotic under some operating conditions for wide range of system parameter values. The reason why the PLL can cause chaos is closely related to the homoclinic orbits of which existence are proved by Melnikov method. In this paper, we review the motivation and significance of chaos occurring in the PLL circuits. Then we confirm various chaotic characteristics of the phase-locked loop equation having the homoclinic orbits such as the fractal basin boundaries and sensitive dependence on initial conditions of a solution. At last, we investigate the route to chaos of the periodic solution of first type (PS1) by calculating the bifurcation diagram, and presents a new results that the PS1 can be chaotic via the period-doubling cascade.},
keywords={},
doi={},
ISSN={},
month={June},}

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TY - JOUR
TI - Homoclinic Orbits, Fractal Basin Boundaries and Bifurcations of Phase-Locked Loop Circuits
T2 - IEICE TRANSACTIONS on transactions
SP - 828
EP - 835
AU - Tetsuro ENDO
PY - 1990
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E73-E
IS - 6
JA - IEICE TRANSACTIONS on transactions
Y1 - June 1990
AB - The phase-locked loop (PLL) is a versatile functional device widely used in many electronic system. We found previously that the PLL can become chaotic under some operating conditions for wide range of system parameter values. The reason why the PLL can cause chaos is closely related to the homoclinic orbits of which existence are proved by Melnikov method. In this paper, we review the motivation and significance of chaos occurring in the PLL circuits. Then we confirm various chaotic characteristics of the phase-locked loop equation having the homoclinic orbits such as the fractal basin boundaries and sensitive dependence on initial conditions of a solution. At last, we investigate the route to chaos of the periodic solution of first type (PS1) by calculating the bifurcation diagram, and presents a new results that the PS1 can be chaotic via the period-doubling cascade.
ER -