Control of delayed feedback over Turing and Hopf bifurcation transformations
This paper studied on the spatiotemporal instability of a class of reaction-diffusion equations under delayed feedback control.In this paper,the impact of delay on Turing and Hopf instability in the vicinity of codimension-2 Turing-Hopf phase space was analyzed,where the time delay was treated as a perturbation.It was found that the presence of delay significantly altered the oscillation frequency,the intrinsic wave vector,and the intensities of both Turing and Hopf modes,which mean that the application of appropriate time delay can modulate the competition between the Turing and Hopf modes.Furthermore,the analysis showed that either single feedback or double feedback can control the transformation between Turing and Hopf patterns,demonstrating the effectiveness of delayed feedback in controlling the formation of patterns near codimension-2 Turing-Hopf phase space.
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