Controlling the transition between the Turing and antispiral patterns by using time-delayed-feedback

Details Controlling the transition between the Turing and antispiral patterns by using time-delayed-feedback Controlling the transition between the Turing and antispiral patterns by using time-delayed-feedback

2011-08-02

arxiv.org/abs/1108.0450v1

Chinese Physics B, 2012,21(3):034701

Nonlinear Sciences

Pattern Formation and Solitons

12 pages, 6 figures

Scientific paper

The controllable transition between the Turing and antispiral patterns is studied by using time-delayed-feedback strategy in a FitzHugh-Nagumo model. We treat the time delay as perturbation and analyze the effect of the time delay on the Turing and Hopf instabilities near the Turing-Hopf codimension-two phase space. Numerical simulations show 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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