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• W2026384090 endingPage "84" @default.
• W2026384090 startingPage "41" @default.
• W2026384090 abstract "Asymptotic and numerical methods are used to highlight different types of dynamical behaviors that occur for the motion of a localized spike‐type solution to the singularly perturbed Gierer–Meinhardt and Schnakenberg reaction‐diffusion models in a one‐dimensional spatial domain. Depending on the parameter range in these models, there can either be a slow evolution of a spike toward the midpoint of the domain, a sudden oscillatory instability triggered by a Hopf bifurcation leading to an intricate temporal oscillation in the height of the spike, or a pulse‐splitting instability leading to the creation of new spikes in the domain. Criteria for the onset of these oscillatory and pulse‐splitting instabilities are obtained through asymptotic and numerical techniques. A moving‐mesh numerical method is introduced to compute these different behaviors numerically, and results are compared with corresponding results computed using a method of lines based software package." @default.
• W2026384090 created "2016-06-24" @default.
• W2026384090 creator A5030873303 @default.
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• W2026384090 date "2003-06-02" @default.
• W2026384090 modified "2023-10-16" @default.
• W2026384090 title "Numerical Challenges for Resolving Spike Dynamics for Two One-Dimensional Reaction-Diffusion Systems" @default.
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• W2026384090 doi "https://doi.org/10.1111/1467-9590.t01-1-00227" @default.
• W2026384090 hasPublicationYear "2003" @default.
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