The problem of self-sustained oscillations in excitable complex networks is the central issue under investigation, among which the prediction and the realization of self-sustained oscillations in different kinds of excitable networks are the challenging tasks. In this paper, we extensively investigate the prediction and the realization of a Winfree loop sustained oscillation (WLSO) in two-dimensional (2D) excitable lattices. By analyzing the network structure, the fundamental oscillation source structure (FOSS) of WLSO in a 2D excitable lattice is exposed explicitly. For the suitable combinations of system parameters, the Winfree loop can self-organize on the FOSS to form an oscillation source sustaining the oscillation, and these suitable parameter combinations are predicted by calculating the minimum Winfree loop length and have been further confirmed in numerical simulations. However, the FOSS cannot spontaneously offer the WLSO in 2D excitable lattices in usual cases due to the coupling bidirectionality and the symmetry properties of the lattice. A targeted protection scheme of the oscillation source is proposed by overcoming these two drawbacks. Finally, the WLSO is realized in the 2D excitable lattice successfully.
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July 2019
Research Article|
July 12 2019
Winfree loop sustained oscillation in two-dimensional excitable lattices: Prediction and realization
Yu Qian;
Yu Qian
a)
1
Nonlinear Research Institute, Baoji University of Arts and Sciences
, Baoji 721007, China
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Gang Zhang;
Gang Zhang
1
Nonlinear Research Institute, Baoji University of Arts and Sciences
, Baoji 721007, China
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Yafeng Wang;
Yafeng Wang
1
Nonlinear Research Institute, Baoji University of Arts and Sciences
, Baoji 721007, China
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Chenggui Yao;
Chenggui Yao
2
Department of Mathematics, Shaoxing University
, Shaoxing 312000, China
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Zhigang Zheng
Zhigang Zheng
b)
3
Institute of Systems Science, Huaqiao University
, Xiamen 361021, China
4
College of Information Science and Engineering, Huaqiao University
, Xiamen 361021, China
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Yu Qian
1,a)
Gang Zhang
1
Yafeng Wang
1
Chenggui Yao
2
Zhigang Zheng
3,4,b)
1
Nonlinear Research Institute, Baoji University of Arts and Sciences
, Baoji 721007, China
2
Department of Mathematics, Shaoxing University
, Shaoxing 312000, China
3
Institute of Systems Science, Huaqiao University
, Xiamen 361021, China
4
College of Information Science and Engineering, Huaqiao University
, Xiamen 361021, China
a)
Electronic mail: [email protected]
b)
Electronic mail: [email protected]
Chaos 29, 073106 (2019)
Article history
Received:
December 13 2018
Accepted:
June 20 2019
Citation
Yu Qian, Gang Zhang, Yafeng Wang, Chenggui Yao, Zhigang Zheng; Winfree loop sustained oscillation in two-dimensional excitable lattices: Prediction and realization. Chaos 1 July 2019; 29 (7): 073106. https://doi.org/10.1063/1.5085644
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