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

doi:10.1088/1674-1056/ac1b83

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

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

Karthikeyan Rajagopal^1,†, Anitha Karthikeyan², and Balamurali Ramakrishnan¹

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 Rajagopal^1,†, Anitha Karthikeyan², and Balamurali Ramakrishnan¹

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/Abstract

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)

Karthikeyan Rajagopal, Anitha Karthikeyan, and Balamurali Ramakrishnan. Controlling chaos and supressing chimeras in a fractional-order discrete phase-locked loop using impulse control[J]. 中国物理B, 2021, 30(12): 120512-120512.

参考文献

[1] de Bellescize H 1932 Onde Electr. 11 230
[2] Banerjee T and Sarkar B C 2005 Signal Process. 85 1139
[3] Banerjee T and Sarkar B C 2005 Signal Process. 85 1611
[4] Stensby J L 1993 J. Franklin Inst. 330 775
[5] Piqueira J R C 2009 Commun. Nonlin. Sci. Numer. Simulat. 14 2328
[6] Best R E 2003 McGraw-Hill, New York
[7] Monteiro L H A, Favaretto Filho D N and Piqueira J R C 2004 IEEE Signal Process. Lett. 11 494
[8] Harb B A and Harb A M 2004 Chaos Solitons & Fractals 19 667
[9] Bernstein G M, Liberman M and Lichtenberg A J 1990 IEEE Trans. Commun. 37 1062
[10] Bernstein G M and Liberman M 1990 IEEE Transactions on Circuits and Systems 37 1157
[11] Tanmoy B and Bishnu C S 2008 AEU-International Journal of Electronics and Communications 62 86
[12] Ding Y and Ye H 2009 Math. Comput. Model. 50 386
[13] Sierociuk D, Skovranek T, Macias M, et al. 2015 Appl. Math. Comput. 257 2
[14] Rajagopal K, Karthikeyan A, Jafari S, Parastesh F, Volos C and Hussain I 2020 Int. J. Mod. Phys. B 34 2050157
[15] Zhou P, Ma J and Tang J 2020 Nonlin. Dyn. 100 2353
[16] Ama N, Martinz F, Matakas L J and Kassab F J 2013 IEEE Trans. Power Electron. 28 144
[17] Leonov G A, Kuznetsov N V, Yuldashev M V and Yuldashev R V 2015 IEEE Transactions on Circuits and Systems I:Regular Papers 62 2454
[18] Kuznetsov N V, Leonov G A, Yuldashev M V and Yuldashev R V 2015 IFAC-PapersOnLine 48 710
[19] Piqueira J R C 2009 Commun. Nonlin. Sci. Numer. Simulat. 14 2328
[20] Piqueira J R C 2017 Commun. Nonlin. Sci. Numer. Simulat. 42 178
[21] Lindsey W C and Chie C M 1981 Proc. IEEE 69 410
[22] Danca M F 2020 Symmetry 12 340
[23] Cheng J 2011 Theory of Fractional Difference Equations (Xiamen:Xiamen University Press)
[24] Wu G C and Baleanu D 2014 Nonlin. Dyn. 75 283
[25] Danca M F, Fečkan M and Kuznetsov N 2019 Nonlin. Dyn.s 98 1219
[26] Bregni S 2002 Synchronization of Digital Telecommunications Networks 1st Edn. (Chichester:John Wiley & Sons)
[27] Williard M W 1970 IEEE Trans. Commun. 18 467
[28] Lindsey W C and Kantak A V 1980 IEEE Trans. Commun. 28 1260
[29] Tavazoei M and Haeri M 2009 Automatica 45 1886
[30] Muni S S and Provata A 2020 Nonlin. Dyn. 101 2509

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

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

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh. An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity[J]. 中国物理B, 2023, 32(3): 30203-030203.
[2]	Xiaodong Jiao(焦晓东), Mingfeng Yuan(袁明峰), Jin Tao(陶金), Hao Sun(孙昊), Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability[J]. 中国物理B, 2023, 32(1): 10507-010507.
[3]	Chunlei Fan(范春雷) and Qun Ding(丁群). A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain[J]. 中国物理B, 2023, 32(1): 10501-010501.
[4]	Xiaopeng Yan(闫晓鹏), Xingyuan Wang(王兴元), and Yongjin Xian(咸永锦). Synchronously scrambled diffuse image encryption method based on a new cosine chaotic map[J]. 中国物理B, 2022, 31(8): 80504-080504.
[5]	Dong-Zhou Zhong(钟东洲), Zhe Xu(徐喆), Ya-Lan Hu(胡亚兰), Ke-Ke Zhao(赵可可), Jin-Bo Zhang(张金波),Peng Hou(侯鹏), Wan-An Deng(邓万安), and Jiang-Tao Xi(习江涛). Multi-target ranging using an optical reservoir computing approach in the laterally coupled semiconductor lasers with self-feedback[J]. 中国物理B, 2022, 31(7): 74205-074205.
[6]	Ai-Xue Qi(齐爱学), Bin-Da Zhu(朱斌达), and Guang-Yi Wang(王光义). Complex dynamic behaviors in hyperbolic-type memristor-based cellular neural network[J]. 中国物理B, 2022, 31(2): 20502-020502.
[7]	Arnold Ngapasare, Georgios Theocharis, Olivier Richoux, Vassos Achilleos, and Charalampos Skokos. Energy spreading, equipartition, and chaos in lattices with non-central forces[J]. 中国物理B, 2022, 31(2): 20506-020506.
[8]	Alireza Bahramian, Sajjad Shaukat Jamal, Fatemeh Parastesh, Kartikeyan Rajagopal, and Sajad Jafari. Collective behavior of cortico-thalamic circuits: Logic gates as the thalamus and a dynamical neuronal network as the cortex[J]. 中国物理B, 2022, 31(2): 28901-028901.
[9]	Wenjie Yang(杨文杰). Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation[J]. 中国物理B, 2022, 31(2): 20201-020201.
[10]	Hsinchen Yu(于心澄), Dong Bai(柏栋), Peishan He(何佩珊), Xiaoping Zhang(张小平), Zhongzhou Ren(任中洲), and Qiang Zheng(郑强). Resonance and antiresonance characteristics in linearly delayed Maryland model[J]. 中国物理B, 2022, 31(12): 120502-120502.
[11]	Liang'an Huo(霍良安) and Xiaomin Chen(陈晓敏). Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model[J]. 中国物理B, 2022, 31(11): 110204-110204.
[12]	Yong-Bing Hu(胡永兵), Xiao-Min Yang(杨晓敏), Da-Wei Ding(丁大为), and Zong-Li Yang(杨宗立). Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application[J]. 中国物理B, 2022, 31(11): 110501-110501.
[13]	Yining Su(苏怡宁), Xingyuan Wang(王兴元), and Shujuan Lin(林淑娟). An image encryption algorithm based on spatiotemporal chaos and middle order traversal of a binary tree[J]. 中国物理B, 2022, 31(11): 110503-110503.
[14]	Yue Li(李月), Zengqiang Chen(陈增强), Zenghui Wang(王增会), and Shijian Cang(仓诗建). Nonlinear dynamics analysis of cluster-shaped conservative flows generated from a generalized thermostatted system[J]. 中国物理B, 2022, 31(1): 10501-010501.
[15]	You-Ming Lei(雷佑铭) and Yan-Yan Han(韩彦彦). Control of chaos in Frenkel-Kontorova model using reinforcement learning[J]. 中国物理B, 2021, 30(5): 50503-050503.