A reaction-diffusion model describing water and plant interaction proposed by Klausmeier is studied. The existence of non-constant steady state solutions shown through bifurcation methods, the large amplitude spatial patterned proved using associated shadow system. It rigorously that non-homogeneous vegetation states exist when rainfall at a lower level in which homogeneous cannot survive. Even...

We establish a series of properties of symmetric, N -pulse, homoclinic solutions of the reduced Gray– Scott system: u′′ = uv2, v′′ = v− uv2, which play a pivotal role in questions concerning the existence and self-replication of pulse solutions of the full Gray–Scott model. Specifically, we establish the existence, and study properties, of solution branches in the (α,β)-plane that represent mul...

The aim of this work is to propose a new numerical approach image restoration and contrast enhancement based on reaction-diffusion model (Gray–Scott model). For noise removal, Lattice Boltzmann technique used. This method usually used in fluid dynamics experiments. Since pixels motion can be compared fluids motion, the presented also indicates good performance processing noisy images. efficienc...

Traditionally reaction-diffusion simulations have been performed on regularly discretised spaces. In an Amorphous Computer [1] the processors are distributed densely but randomly. By implementing the Gray-Scott model on an amorphous computer simulation, we show that the patterns obtained by uniform discretisation can also be realised qualitatively on irregular, amorphous discretisations if diff...