Turing Instabilities at Hopf Bifurcation

@article{Ricard2009TuringIA,
  title={Turing Instabilities at Hopf Bifurcation},
  author={M. R. Ricard and S. Mischler},
  journal={J. Nonlinear Science},
  year={2009},
  volume={19},
  pages={467-496}
}
Turing–Hopf instabilities for reaction-diffusion systems provide spatially inhomogeneous time-periodic patterns of chemical concentrations. In this paper we suggest a way for deriving asymptotic expansions to the limit cycle solutions due to a Hopf bifurcation in two-dimensional reaction systems and we use them to build convenient normal modes for the analysis of Turing instabilities of the limit cycle. They extend the Fourier modes for the steady state in the classical Turing approach, as they… CONTINUE READING
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