Attractors with controllable basin sizes from cooperation of contracting and expanding dynamics in pulse-coupled oscillators

doi:10.1088/1674-1056/28/1/010502

中国物理B ›› 2019, Vol. 28 ›› Issue (1): 10502-010502.doi: 10.1088/1674-1056/28/1/010502

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

Attractors with controllable basin sizes from cooperation of contracting and expanding dynamics in pulse-coupled oscillators

Hai-Lin Zou(邹海林) Zi-Chen Deng(邓子辰)

School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710072, China

收稿日期:2018-09-04 修回日期:2018-10-22 出版日期:2019-01-05 发布日期:2019-01-05
通讯作者: Hai-Lin Zou E-mail:zouhailin@nwpu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11502200 and 91648101) and the Fundamental Research Funds for the Central Universities, China (Grant No. 3102018zy012).

Attractors with controllable basin sizes from cooperation of contracting and expanding dynamics in pulse-coupled oscillators

Hai-Lin Zou(邹海林) Zi-Chen Deng(邓子辰)

School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710072, China

Received:2018-09-04 Revised:2018-10-22 Online:2019-01-05 Published:2019-01-05
Contact: Hai-Lin Zou E-mail:zouhailin@nwpu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11502200 and 91648101) and the Fundamental Research Funds for the Central Universities, China (Grant No. 3102018zy012).

摘要/Abstract

摘要：

Unstable attractors are a novel type of attractor with local unstable dynamics, but with positive measures of basins. Here, we introduce local contracting dynamics by slightly modifying the function which mediates the interactions among the oscillators. Thus, the property of unstable attractors can be controlled through the cooperation of expanding and contracting dynamics. We demonstrate that one certain type of unstable attractor is successfully controlled through this simple modification. Specifically, the staying time for unstable attractors can be prolonged, and we can even turn the unstable attractors into stable attractors with predictable basin sizes. As an application, we demonstrate how to realize the switching dynamics that is only sensitive to the finite size perturbations.

关键词: unstable attractors, switching dynamics, pulse-coupled oscillators

Abstract:

Key words: unstable attractors, switching dynamics, pulse-coupled oscillators

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Xt (Synchronization; coupled oscillators) 87.19.lj (Neuronal network dynamics)

邹海林, 邓子辰. Attractors with controllable basin sizes from cooperation of contracting and expanding dynamics in pulse-coupled oscillators[J]. 中国物理B, 2019, 28(1): 10502-010502.

Hai-Lin Zou(邹海林) Zi-Chen Deng(邓子辰). Attractors with controllable basin sizes from cooperation of contracting and expanding dynamics in pulse-coupled oscillators[J]. Chin. Phys. B, 2019, 28(1): 10502-010502.

参考文献 26

[1]	Edward O 2002 Chaos in Dynamical Systems (2nd Edn.) (Cambridge: Cambridge University Press)
[2]	Zhang G T and Wang F Q 2018 Chin. Phys. B 27 018201 doi: 10.1088/1674-1056/27/1/018201
[3]	Dudkowski D, Jafari S, Kapitaniak T, Kuznetsov N V, Leonov G A and Prasad A 2016 Physics Reports 637 1 doi: 10.1016/j.physrep.2016.05.002
[4]	Bao J H and Chen D D 2017 Chin. Phys. B 26 080201 doi: 10.1088/1674-1056/26/8/080201
[5]	Tang Y X, Khalaf A J M and Rajagopal 2018 Chin. Phys. B 27 040502 doi: 10.1088/1674-1056/27/4/040502
[6]	Wang Y, Zheng G C and Liu C X 2018 Acta Physica Sinica 67 050502
[7]	Schittler Neves F and Timme M 2012 Phys. Rev. Lett. 109 018701 doi: 10.1103/PhysRevLett.109.018701
[8]	Timme M, Wolf F and Geisel T 2002 Phys. Rev. Lett. 89 154105 doi: 10.1103/PhysRevLett.89.154105
[9]	Timme M, Wolf F and Geisel T 2003 Chaos 13 377 doi: 10.1063/1.1501274
[10]	Ashwin P and Timme M 2005 Nonlinearity 18 2035 doi: 10.1088/0951-7715/18/5/009
[11]	Milnor J 1985 Commun. Math. Phys. 99 177 doi: 10.1007/BF01212280
[12]	Broer H, Efstathiou K and Subramanian E 2008 Nonlinearity 21 1385 doi: 10.1088/0951-7715/21/6/014
[13]	Zou H L, Deng Z C, Hu W P, Aihara K and Lai Y C 2017 Nonlinear Dyn. 89 887 doi: 10.1007/s11071-017-3490-5
[14]	Mirollo R E and Strogatz S H 1990 SIAM J. Appl. Math. 50 1645 doi: 10.1137/0150098
[15]	Tsodyks M, Mitkov I and Sompolinsky H 1993 Phys. Rev. Lett. 71 1280 doi: 10.1103/PhysRevLett.71.1280
[16]	Vreeswijk C V 1996 Phys. Rev. E 54 5522 doi: 10.1103/PhysRevE.54.5522
[17]	Gerstner W 1996 Phys. Rev. Lett. 76 1755 doi: 10.1103/PhysRevLett.76.1755
[18]	Kanamaru T and Aihara K 2010 Neural Comp. 22 1383 doi: 10.1162/neco.2010.04-09-997
[19]	Luccioli S and Politi A 2010 Phys. Rev. Lett. 105 158104 doi: 10.1103/PhysRevLett.105.158104
[20]	Zou H, Gong X and Lai C H 2010 Phys. Rev. E 82 046209 doi: 10.1103/PhysRevE.82.046209
[21]	Zou H L, Li M, Lai C H and Lai Y C 2012 Phys. Rev. E 86 066214 doi: 10.1103/PhysRevE.86.066214
[22]	Kirst C and Timme M 2008 Phys. Rev. E 78 065201(R)
[23]	Schittler Neves F and Timme M 2009 J. Phys. A: Math. Theo. 42 345103 doi: 10.1088/1751-8113/42/34/345103
[24]	Zou H L, Katori Y, Deng Z C, Aihara K and Lai Y C 2015 Chaos 25 103109 doi: 10.1063/1.4930840
[25]	Hartle H and Wackerbauer R 2017 Phys. Rev. E 96 032223 doi: 10.1103/PhysRevE.96.032223
[26]	Ashwin P, Creaser J and Tsanevaatanasova K 2018 arXiv 1804.00550

Attractors with controllable basin sizes from cooperation of contracting and expanding dynamics in pulse-coupled oscillators

Attractors with controllable basin sizes from cooperation of contracting and expanding dynamics in pulse-coupled oscillators

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 26

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]	Xinyu Gao(高昕瑜), Bo Sun(孙博), Yinghong Cao(曹颖鸿), Santo Banerjee, and Jun Mou(牟俊). A color image encryption algorithm based on hyperchaotic map and DNA mutation[J]. 中国物理B, 2023, 32(3): 30501-030501.
[3]	Huamei Yang(杨华美) and Yuangen Yao(姚元根). Realizing reliable XOR logic operation via logical chaotic resonance in a triple-well potential system[J]. 中国物理B, 2023, 32(2): 20501-020501.
[4]	Zhixuan Yuan(袁治轩), Mengmeng Du(独盟盟), Yangyang Yu(于羊羊), and Ying Wu(吴莹). Epilepsy dynamics of an astrocyte-neuron model with ammonia intoxication[J]. 中国物理B, 2023, 32(2): 20502-020502.
[5]	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.
[6]	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.
[7]	Qiankun Sun(孙乾坤), Shaobo He(贺少波), Kehui Sun(孙克辉), and Huihai Wang(王会海). A novel hyperchaotic map with sine chaotification and discrete memristor[J]. 中国物理B, 2022, 31(12): 120501-120501.
[8]	Hongwei Zhang(张红伟), Ran Cheng(程然), and Dawei Ding(丁大为). Finite-time synchronization of uncertain fractional-order multi-weighted complex networks with external disturbances via adaptive quantized control[J]. 中国物理B, 2022, 31(10): 100504-100504.
[9]	Zhi-Wei Jia(贾志伟), Li Li(李丽), Yi-Yan Guo(郭一岩), An-Bang Wang(王安帮), Hong Han(韩红), Jin-Chuan Zhang(张锦川), Pu Li(李璞), Shen-Qiang Zhai(翟慎强), and Feng-Qi Liu(刘峰奇). Periodic and chaotic oscillations in mutual-coupled mid-infrared quantum cascade lasers[J]. 中国物理B, 2022, 31(10): 100505-100505.
[10]	Rui Wang(王蕊), Meng-Yang Li(李孟洋), and Hai-Jun Luo(罗海军). Exponential sine chaotification model for enhancing chaos and its hardware implementation[J]. 中国物理B, 2022, 31(8): 80508-080508.
[11]	Gang Zhang(张刚), Yu-Jie Zeng(曾玉洁), and Zhong-Jun Jiang(蒋忠均). Characteristics of piecewise linear symmetric tri-stable stochastic resonance system and its application under different noises[J]. 中国物理B, 2022, 31(8): 80502-080502.
[12]	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.
[13]	Yi-Xuan Shan(单仪萱), Hui-Lan Yang(杨惠兰), Hong-Bin Wang(王宏斌), Shuai Zhang(张帅), Ying Li(李颖), and Gui-Zhi Xu(徐桂芝). Effect of astrocyte on synchronization of thermosensitive neuron-astrocyte minimum system[J]. 中国物理B, 2022, 31(8): 80507-080507.
[14]	Li-Fang He(贺利芳), Qiu-Ling Liu(刘秋玲), and Tian-Qi Zhang(张天骐). Research and application of stochastic resonance in quad-stable potential system[J]. 中国物理B, 2022, 31(7): 70503-070503.
[15]	Sheng-Hao Jia(贾生浩), Yu-Xia Li(李玉霞), Qing-Yu Shi(石擎宇), and Xia Huang(黄霞). Design and FPGA implementation of a memristor-based multi-scroll hyperchaotic system[J]. 中国物理B, 2022, 31(7): 70505-070505.