Pattern transitions induced by delay feedback.

Modulated by delay feedback (DF), a reaction-diffusion system is destabilized and undergoes pattern transitions in the parametric region where the undelayed system spontaneously exhibits a bulk oscillation. By varying the feedback parameters, oscillatory hexagon superlattices and stripes, as well as stationary hexagons are observed. Meanwhile, the hexagon superlattices with different wavelengths are found under appropriate feedback parameters. It is demonstrated that, since the DF induces an instability of homogeneous limit cycle with respect to spatial perturbations, the patterns possessing the corresponding spatial modes are formed. Instead of stabilizing the system, here the DF may play a role of destabilization.

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