Slow translational instabilities of spike patterns in the one-dimensional Gray-Scott model
نویسندگان
چکیده
منابع مشابه
Spike autosolitons in the Gray-Scott model
We performed a comprehensive study of the spike autosolitons: self-sustained solitary inhomogeneous states, in the classical reaction-diffusion system — the GrayScott model. We developed singular perturbation techniques based on the strong separation of the length scales to construct asymptotically the solutions in the form of a one-dimensional static autosolitons, higher-dimensional radially-s...
متن کاملPattern formation in the one-dimensional Gray - Scott model
In this work, we analyse a pair of one-dimensional coupled reaction-diffusion equations known as the Gray–Scott model, in which self-replicating patterns have been observed. We focus on stationary and travelling patterns, and begin by deriving the asymptotic scaling of the parameters and variables necessary for the analysis of these patterns. Single-pulse and multipulse stationary waves are sho...
متن کاملSpike autosolitons in Gray-Scott model
We performed a comprehensive study of spike autosolitons: highly localized solitary states, in the classical reaction-diffusion system — the Gray-Scott model. We developed singular perturbation techniques based on the strong separation of length scales to construct asymptotically the solutions in the form of one-dimensional and higher-dimensional radially-symmetric static autosolitons, and two ...
متن کاملSpike autosolitons and pattern formation scenarios in the two-dimensional Gray-Scott model
We performed an extensive numerical study of pattern formation scenarios in the twodimensional Gray-Scott reaction-diffusion model. We concentrated on the parameter region in which there exists a strong separation of length and/or time scales. We found that the static one-dimensional autosolitons (stripes) break up into two-dimensional radially-symmetric autosolitons (spots). The traveling one-...
متن کاملControl of spatiotemporal patterns in the Gray-Scott model.
This paper studies the effects of a time-delayed feedback control on the appearance and development of spatiotemporal patterns in a reaction-diffusion system. Different types of control schemes are investigated, including single-species, diagonal, and mixed control. This approach helps to unveil different dynamical regimes, which arise from chaotic state or from traveling waves. In the case of ...
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ژورنال
عنوان ژورنال: Interfaces and Free Boundaries
سال: 2006
ISSN: 1463-9963
DOI: 10.4171/ifb/140