RETRACTED ARTICLE: Slowly Modulated Two-Pulse Solutions in a Generalized Klausmeier–Gray–Scott Model
نویسندگان
چکیده
منابع مشابه
Slowly-modulated two pulse solutions and pulse splitting bifurcations
Two pulse solutions play a central role in the phenomena of self-replicating pulses in 1-D reaction-diiusion systems. In this work, we focus on the 1-D Gray-Scott model as a prototype. We carry out an existence and stability study for solutions consisting of two pulses moving apart from each other with slowly varying velocities. In the various parameter regimes, critical maximum wave speeds are...
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Two pulse solutions play a central role in the phenomena of self-replicating pulses in the one-dimensional (1-D) Gray–Scott model. In the present work (part I of two parts), we carry out an existence study for solutions consisting of two symmetric pulses moving apart from each other with slowly varying velocities. This corresponds to a “mildly strong” pulse interaction problem in which the inhi...
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In this second paper, we develop a geometrical method to systematically study the singular perturbed problem associated to slowly modulated two-pulse solutions. It enables one to see that the characteristics of these solutions are strongly determined by the flow on a slow manifold and, hence, also to identify the saddle-node bifurcations and bifurcations to classical traveling waves in which th...
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ژورنال
عنوان ژورنال: Bulletin of the Malaysian Mathematical Sciences Society
سال: 2016
ISSN: 0126-6705,2180-4206
DOI: 10.1007/s40840-016-0303-9