Well-posedness in $ L_\infty of the nonlocal Gray-Scott model is studied for integrable kernels, along with stability semi-trivial spatially homogeneous steady state. In addition, it shown that solutions to system converge those classical diffusive limit.

Gray, Scott and their collaborators proposed the model analyzed in our paper in the 80’s. The model describes an autocatalytic mechanism in isothermal systems where the reaction rate is increased by strengthening the concentration of one of the products. The chemical reaction (Fig. 1) occurs in a continuously stirred tank reactor (CSTR) and it involves two reactants X and Y with concentrations ...

We discovered a type of spiral wave solutions in reaction-diffusion systems--spike spiral wave, which significantly differs from the spiral waves observed in the models of FitzHugh-Nagumo type. We present an asymptotic theory of these waves in the Gray-Scott model [Chem. Sci. Eng. 38, 29 (1983)]. We derive the kinematic relations describing the shape of this spiral, and find the dependence of i...

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 ...

In this work, we analyze a pair of one-dimensional coupled reaction-diiusion equations known as the Gray{Scott model, in which self-replicating patterns have been observed. We focus on stationary and traveling patterns, and begin by deriving the asymptotic scaling of the parameters and variables necessary for the analysis of these patterns. Single{pulse and multiple{pulse stationary waves are s...

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...