| ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS |
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Controlling the transition between Turing and antispiral patterns by using time-delayed-feedback |
| He Ya-Feng(贺亚峰), Liu Fu-Cheng(刘富成), Fan Wei-Li(范伟丽), and Dong Li-Fang(董丽芳)† |
| Hebei Key Laboratory of Optic-electronic Information Materials, College of Physical Science and Technology, Hebei University, Baoding 071002, China |
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Abstract The controllable transition between Turing and antispiral patterns is studied by using a time-delayed-feedback strategy in a FitzHugh-Nagumo model. We treat the time delay as a perturbation and analyse the effect of the time delay on the Turing and Hopf instabilities near the Turing-Hopf codimension-two phase space. Numerical simulations show that the transition between the Turing patterns (hexagon, stripe, and honeycomb), the dual-mode antispiral, and the antispiral by applying appropriate feedback parameters. The dual-mode antispiral pattern originates from the competition between the Turing and Hopf instabilities. Our results have shown the flexibility of the time delay on controlling the pattern formations near the Turing-Hopf codimension-two phase space.
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Received: 24 July 2011
Revised: 18 August 2011
Accepted manuscript online:
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PACS:
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47.54.-r
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(Pattern selection; pattern formation)
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82.40.Ck
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(Pattern formation in reactions with diffusion, flow and heat transfer)
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82.40.Bj
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(Oscillations, chaos, and bifurcations)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10975043 and 10947166), the Natural Science Foundation of Hebei Province, China (Grant Nos. A2011201006 and A2010000185), and the Science Foundation of Hebei University. |
Corresponding Authors:
Dong Li-Fang,Donglf@hbu.edu.cn
E-mail: Donglf@hbu.edu.cn
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Cite this article:
He Ya-Feng(贺亚峰), Liu Fu-Cheng(刘富成), Fan Wei-Li(范伟丽), and Dong Li-Fang(董丽芳) Controlling the transition between Turing and antispiral patterns by using time-delayed-feedback 2012 Chin. Phys. B 21 034701
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