| Abstract: |
| In this talk, we derive the normal form for the Turing-Turing-Hopf (or, $0^{2} : \pm \mathrm{i} \omega$) bifurcation from a two-components reaction-diffusion system. Usually, two-components reaction-diffusion systems have cxdimension-two bifurcation. Although, if we add a parameter to the reaction term, then the system can have codimension-three bifurcation. We will see that the Turing-Turing-Hopf bifurcation induces the traveling waves, modulated traveling waves, heteroclinic cycles, invariant surfaces and chaotic dynamics. Furthermore, some numerical experiments for the reaction-diffusion system and the normal form will be shown. |
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