Anomalous Scaling of Hopf Bifurcation Thresholds for the Stability of Localized Spot Patterns for Reaction-Diffusion Systems in 2-D J .

@inproceedings{Tzou2017AnomalousSO,
  title={Anomalous Scaling of Hopf Bifurcation Thresholds for the Stability of Localized Spot Patterns for Reaction-Diffusion Systems in 2-D J .},
  author={J. C. Tzou and Michael J. Ward and Jun Cheng Wei},
  year={2017}
}
For three specific singularly perturbed two-component reaction diffusion systems in a bounded 2-D domain admitting localized multi-spot patterns, we provide a detailed analysis of the parameter values for the onset of temporal oscillations of the spot amplitudes. The two key bifurcation parameters in each of the RD systems are the reaction-time parameter τ and the inhibitor diffusivity D. In the limit of large diffusivity D = D0/ν ≫ 1, with D0 = O(1), ν ≡ −1/ log ε and ε denoting the activator… CONTINUE READING

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