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Control of the spatiotemporal pattern with time delayed feedback in a gas discharge system is studied both analytically and numerically. The time delay in the semiphenomenological model is reduced as a perturbation. Based on the linear stability analysis, the effects of the time delay on the Turing and the Hopf modes near the Turing-Hopf codimension-two phase space are investigated. Then, the relations between the parameters of feedback and the oscillatory frequency, and the critical wavelength of the system are obtained. Results show that the transition between patterns can be controlled effectively by applying appropriate feedback even when the applied voltage keeps constant. The consequence of increasing the feedback intensity or the delayed time is equivalent to increasing the applied voltage. Furthermore, the analytical results are verified by two-dimensional numerical simulation. Our work proposes a way to control the pattern formation in a gas discharge system.
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Keywords:
- gas discharge /
- pattern formation /
- time delayed feedback
[1] Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[2] Service R F 1999 Science 286 1067
[3] Gotoh H, Kamada H, Saitoh T, Shigemori S, Temmyo J 2004 Appl. Phys. Lett. 85 2836
[4] Nattel S 2002 Nature 415 219
[5] Zykov V S, Bordiougov G, Brandtstädter H, Gerdes I, Engel H 2003 Phys. Rev. E 68 016214
[6] Chen J X, Xu J R, Yuan X P, Ying H P 2009 J. Phys. Chem. B 113 849
[7] Sternbock O, Schtze J, Mller S C 1992 Phys. Rev. Lett. 68 248
[8] Schneider F M, Schöll E, Dahlem M A 2009 Chao 19 015110
[9] Tung C K, Chan C K 2002 Phys. Rev. Lett. 89 248302
[10] Mikhailov A S, Showalter K 2006 Phys. Rep. 425 79
[11] Guo W Q, Qiao C, Zhang Z M, Ouyang Q, Wang H L 2010 Phys. Rev. E 81 056214
[12] He Y F, Dong L F, Liu F C, Fan W L 2005 Acta Phys. Sin. 54 4236 (in Chinese) [贺亚峰, 董丽芳, 刘富成, 范伟丽 2005 物理学报 54 4236]
[13] He Y F, Dong L F, Liu W L, Wang H F, Zhao Z C, Fan W L 2007 Phys. Rev. E 76 017203
[14] Dong L F, Fan W L, Wang S, Ji Y F, Liu Z W, Chen Q 2011 Phys. Plasmas 18 033506
[15] Dong L F, Li B, Lu N, Li X C, Shen Z K 2012 Phys. Plasmas 19 052304
[16] Dong L F, Yang Y J, Li B, Fan W L, Song Q 2011 Phys. Plasmas 18 122101
[17] Astrov Yu A, Logvin Yu A 1997 Phys. Rev. Lett. 79 2983
[18] Ammelt E, Astrov Yu A, Purwins H G 1998 Phys. Rev. E 58 7109
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[1] Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[2] Service R F 1999 Science 286 1067
[3] Gotoh H, Kamada H, Saitoh T, Shigemori S, Temmyo J 2004 Appl. Phys. Lett. 85 2836
[4] Nattel S 2002 Nature 415 219
[5] Zykov V S, Bordiougov G, Brandtstädter H, Gerdes I, Engel H 2003 Phys. Rev. E 68 016214
[6] Chen J X, Xu J R, Yuan X P, Ying H P 2009 J. Phys. Chem. B 113 849
[7] Sternbock O, Schtze J, Mller S C 1992 Phys. Rev. Lett. 68 248
[8] Schneider F M, Schöll E, Dahlem M A 2009 Chao 19 015110
[9] Tung C K, Chan C K 2002 Phys. Rev. Lett. 89 248302
[10] Mikhailov A S, Showalter K 2006 Phys. Rep. 425 79
[11] Guo W Q, Qiao C, Zhang Z M, Ouyang Q, Wang H L 2010 Phys. Rev. E 81 056214
[12] He Y F, Dong L F, Liu F C, Fan W L 2005 Acta Phys. Sin. 54 4236 (in Chinese) [贺亚峰, 董丽芳, 刘富成, 范伟丽 2005 物理学报 54 4236]
[13] He Y F, Dong L F, Liu W L, Wang H F, Zhao Z C, Fan W L 2007 Phys. Rev. E 76 017203
[14] Dong L F, Fan W L, Wang S, Ji Y F, Liu Z W, Chen Q 2011 Phys. Plasmas 18 033506
[15] Dong L F, Li B, Lu N, Li X C, Shen Z K 2012 Phys. Plasmas 19 052304
[16] Dong L F, Yang Y J, Li B, Fan W L, Song Q 2011 Phys. Plasmas 18 122101
[17] Astrov Yu A, Logvin Yu A 1997 Phys. Rev. Lett. 79 2983
[18] Ammelt E, Astrov Yu A, Purwins H G 1998 Phys. Rev. E 58 7109
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