A Fractional-Order Phase-Locked Loop with Time-Delay and Its Hopf Bifurcation  

作　　者：YU Ya-Juan WANG Zai-Hua 俞亚娟;王在华(State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics,Nanjing 210016;School of Mathematics and Physics,Changzhou University,Changzhou 213164;Institute of Science,PLA University of Science and Technology,Nanjing 211101)

机构地区：[1]State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics,Nanjing 210016 [2]School of Mathematics and Physics,Changzhou University,Changzhou 213164 [3]Institute of Science,PLA University of Science and Technology,Nanjing 211101

出　　处：《Chinese Physics Letters》2013年第11期1-5,共5页中国物理快报（英文版）

基　　金：Supported by the National Natural Science Foundation of China under Grant No 10825207;the Priority Academic Program Development of Jiangsu Higher Education Institutions.

摘　　要：A fractional-order phase-locked loop(PLL)with a time-delay is firstly proposed on the basis of the fact that a capacitor has memory.The existence of Hopf bifurcation of the fractional-order PLL with a time-delay is investigated by studying the root location of the characteristic equation,and the bifurcated periodic solution and its stability are studied simply by using"pseudo-oscillator analysis".The results are checked by numerical simulation.It is found that the fractional-order PLL with a time-delay reduces the locking time,and it minimizes the amplitude of the bifurcated periodic solution when the order is properly chosen.

关 键 词：FRACTIONAL HOPF delay 

分 类 号：O17[理学—数学]