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Existence uniqueness and asymptotic stability of periodic solutions of a nonlinear equation in phase locked technology

Existence uniqueness and asymptotic stability of periodic solutions of a nonlinear equation in... Vol. 7 No. 1 ACTA MATHEMATICAE APPLICATAE SIN~CA Jan., 1991 ~ g EXISTENCE UNIQUENESS AND ASYMPTOTIC STABILITY OF PERIODIC SOLUTIONS OF A NONLINEAR. EQUATION IN PHASE LOCKED TECHNOLOGY Jr~ Ju~ (~ ~) (5%anghai Teach~r~ Unive~'sity) In [1] and [2], %he authors made a deep quali%a~ive analysis of %he equa%ion ~i%h %he character of %angen% de%eo%ed phase and %hey mathema%ically provided a theore%ical basis of why the phase locked loop has no lock-losing poin%. However, according %o many prao%ical express, i% is ra%her diflicul% %o pu% such a phase locked loop in%o practice, %hough i% has fine properties. W. (3. Lindsey [3] made a eireu2% design wi~h the character of detected phase where (l÷~)sin~ (0<~<1). (1) g(~)= l+k cos ~ He pointed cub %ha% such a oiroui~ can be effec~ed practically. One can see bha% in (1) g(~)-~2 ~g ~ when 2--1, and %his is just %he oharac%er of the Sangent de%ee%ed phase described in [1] and [2]. Moreover, when k=0, i% becomes %he resu1% in [4] and [5]. So %he study of %he phase locked loop equation with the charao%0r of %he de~ec%ed phase (1) is of practical significance. In this paper, we consider %he exis%ence, uniqueness and asymptotic http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Existence uniqueness and asymptotic stability of periodic solutions of a nonlinear equation in phase locked technology

Acta Mathematicae Applicatae Sinica , Volume 7 (1) – Jul 13, 2005

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Publisher
Springer Journals
Copyright
Copyright © 1991 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02080207
Publisher site
See Article on Publisher Site

Abstract

Vol. 7 No. 1 ACTA MATHEMATICAE APPLICATAE SIN~CA Jan., 1991 ~ g EXISTENCE UNIQUENESS AND ASYMPTOTIC STABILITY OF PERIODIC SOLUTIONS OF A NONLINEAR. EQUATION IN PHASE LOCKED TECHNOLOGY Jr~ Ju~ (~ ~) (5%anghai Teach~r~ Unive~'sity) In [1] and [2], %he authors made a deep quali%a~ive analysis of %he equa%ion ~i%h %he character of %angen% de%eo%ed phase and %hey mathema%ically provided a theore%ical basis of why the phase locked loop has no lock-losing poin%. However, according %o many prao%ical express, i% is ra%her diflicul% %o pu% such a phase locked loop in%o practice, %hough i% has fine properties. W. (3. Lindsey [3] made a eireu2% design wi~h the character of detected phase where (l÷~)sin~ (0<~<1). (1) g(~)= l+k cos ~ He pointed cub %ha% such a oiroui~ can be effec~ed practically. One can see bha% in (1) g(~)-~2 ~g ~ when 2--1, and %his is just %he oharac%er of the Sangent de%ee%ed phase described in [1] and [2]. Moreover, when k=0, i% becomes %he resu1% in [4] and [5]. So %he study of %he phase locked loop equation with the charao%0r of %he de~ec%ed phase (1) is of practical significance. In this paper, we consider %he exis%ence, uniqueness and asymptotic

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

References