Complex dynamics of a frequency-phase lock system

Author

Ponomarenko, Valery P. ; Tikhonov, Evgeny A.

Author_Institution

Res. Inst. of Appl. Math. & Cybern., Nizhni Novgorod, Russia

fYear

2005

fDate

24-26 Aug. 2005

Firstpage

459

Lastpage

463

Abstract

A nonlinear frequency-phase lock system with second-order filters in control circuits is considered. Dynamic states and bifurcations in this system are investigated using a dynamic model with 2.5 degrees of freedom in the cylindrical phase space. Conditions of synchronous mode stability and the locking domain boundaries are determined. The existence of various regular and chaotic asynchronous modes is revealed, and their behavior under parameter variation is studied. Results are presented using a two-parameter portrait of motions, one-parameter bifurcation diagrams, and phase portraits of attractors.

Keywords

bifurcation; chaos; filters; frequency locked loops; nonlinear dynamical systems; phase locked loops; attractor phase portrait; chaotic asynchronous mode; complex dynamics; control circuits; cylindrical phase space; degrees of freedom; locking domain boundary; nonlinear frequency-phase lock system; one-parameter bifurcation diagram; parameter variation; second-order filter; synchronous mode stability; two-parameter portrait; Bifurcation; Chaos; Circuits; Control systems; Cybernetics; Filters; Frequency; Mathematics; Nonlinear control systems; Nonlinear dynamical systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Physics and Control, 2005. Proceedings. 2005 International Conference

Print_ISBN

0-7803-9235-3

Type

conf

DOI

10.1109/PHYCON.2005.1514027

Filename

1514027