中国物理B ›› 2021, Vol. 30 ›› Issue (12): 120512-120512.doi: 10.1088/1674-1056/ac1b83

所属专题: SPECIAL TOPIC — Interdisciplinary physics: Complex network dynamics and emerging technologies

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Controlling chaos and supressing chimeras in a fractional-order discrete phase-locked loop using impulse control

Karthikeyan Rajagopal1,†, Anitha Karthikeyan2, and Balamurali Ramakrishnan1   

  1. 1 Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, India;
    2 Department of Electronics and Communication Engineering, Prathyusha Engineering College, Chennai, India
  • 收稿日期:2021-03-16 修回日期:2021-06-11 接受日期:2021-08-07 出版日期:2021-11-15 发布日期:2021-11-30
  • 通讯作者: Karthikeyan Rajagopal E-mail:rkarthiekeyan@gmail.com
  • 基金资助:
    Project supported by the Center for Nonlinear Systems, Chennai Institute of Technology, India (Grant No. CIT/CNS/2020/RD/061).

Controlling chaos and supressing chimeras in a fractional-order discrete phase-locked loop using impulse control

Karthikeyan Rajagopal1,†, Anitha Karthikeyan2, and Balamurali Ramakrishnan1   

  1. 1 Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, India;
    2 Department of Electronics and Communication Engineering, Prathyusha Engineering College, Chennai, India
  • Received:2021-03-16 Revised:2021-06-11 Accepted:2021-08-07 Online:2021-11-15 Published:2021-11-30
  • Contact: Karthikeyan Rajagopal E-mail:rkarthiekeyan@gmail.com
  • Supported by:
    Project supported by the Center for Nonlinear Systems, Chennai Institute of Technology, India (Grant No. CIT/CNS/2020/RD/061).

摘要: A fractional-order difference equation model of a third-order discrete phase-locked loop (FODPLL) is discussed and the dynamical behavior of the model is demonstrated using bifurcation plots and a basin of attraction. We show a narrow region of loop gain where the FODPLL exhibits quasi-periodic oscillations, which were not identified in the integer-order model. We propose a simple impulse control algorithm to suppress chaos and discuss the effect of the control step. A network of FODPLL oscillators is constructed and investigated for synchronization behavior. We show the existence of chimera states while transiting from an asynchronous to a synchronous state. The same impulse control method is applied to a lattice array of FODPLL, and the chimera states are then synchronized using the impulse control algorithm. We show that the lower control steps can achieve better control over the higher control steps.

关键词: discrete Josephson junction, fractional order, chaos, impulse control, chimera

Abstract: A fractional-order difference equation model of a third-order discrete phase-locked loop (FODPLL) is discussed and the dynamical behavior of the model is demonstrated using bifurcation plots and a basin of attraction. We show a narrow region of loop gain where the FODPLL exhibits quasi-periodic oscillations, which were not identified in the integer-order model. We propose a simple impulse control algorithm to suppress chaos and discuss the effect of the control step. A network of FODPLL oscillators is constructed and investigated for synchronization behavior. We show the existence of chimera states while transiting from an asynchronous to a synchronous state. The same impulse control method is applied to a lattice array of FODPLL, and the chimera states are then synchronized using the impulse control algorithm. We show that the lower control steps can achieve better control over the higher control steps.

Key words: discrete Josephson junction, fractional order, chaos, impulse control, chimera

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.45.Gg (Control of chaos, applications of chaos) 05.45.Xt (Synchronization; coupled oscillators) 05.45.Pq (Numerical simulations of chaotic systems)