Control of the patterns by using time-delayed feedback near the codimension-three Turing–Hopf–Wave bifurcations

doi:10.1088/1674-1056/22/12/120503

Abstract Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the system shows that the competition among the Turing-, Hopf- and Wave-modes, the wavenumber, and the oscillation frequency of patterns can be controlled by changing the feedback parameters. The role of the feedback intensity P_u played on controlling the pattern competition is equivalent to that of P_w, but opposite to that of P_v. The role of the feedback intensity P_u played on controlling the wavenumber and oscillation frequency of patterns is equivalent to that of P_v, but opposite to that of P_w. When the intensities of feedback are applied equally, changing the delayed time could not alter the competition among these modes, however, it can control the oscillation frequency of patterns. The analytical results are verified by two-dimensional (2D) numerical simulations.

Keywords: pattern formation reaction diffusion system time-delayed feedback

Received: 27 July 2013
Revised: 22 September 2013
Accepted manuscript online:

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	82.40.Ck	(Pattern formation in reactions with diffusion, flow and heat transfer)
	47.54.-r	(Pattern selection; pattern formation)

Fund: Project supported by the National Nature Science Foundation of China (Grant No. 11205044) and the Fundamental Research Funds for the Central Universities (Grant No. 10ML40).

Corresponding Authors: Wang Hui-Juan
E-mail: whuijuanmail@126.com

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Wang Hui-Juan (王慧娟), Wang Yong-Jie (王永杰), Ren Zhi (任芝) Control of the patterns by using time-delayed feedback near the codimension-three Turing–Hopf–Wave bifurcations 2013 Chin. Phys. B 22 120503

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Control of the patterns by using time-delayed feedback near the codimension-three Turing–Hopf–Wave bifurcations

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