in this work, we analyse a pair of two-dimensional coupled reaction-diusion equations known as the gray-scott model, in which spot patterns have been observed. we focus on stationary patterns, and begin by deriving the asymptotic scaling of the parameters and variables necessary for the analysis of these patterns. a complete bifurcation study of these solutions is presented. the main mathematic...

Abstract In this paper, we investigate the spatiotemporal patterns of a freshwater tussock sedge model with discrete time and space variables. We first analyze kinetic system show parametric conditions for flip Neimark–Sacker bifurcations respectively. With spatial diffusion, then that obtained stable homogeneous solutions can experience Turing instability under certain conditions. Through nume...

We describe a necessary condition for zero-eigenvalue Turing instability, i.e., Turing instability arising from a real eigenvalue changing sign from negative to positive, for general chemical reaction networks modeled with mass-action kinetics. The reaction mechanisms are represented by the species-reaction graph (SR graph), which is a bipartite graph with different nodes representing species a...

In this paper, a semi-discrete Brusselator system is considered. The Turing instability theory analysis will be given for the model, then Turing instability conditions can be deduced combining linearization method and inner product technique. A series of numerical simulations of the system are performed in the Turing instability region, various patterns such as square, labyrinthine, spotlike pa...

the present paper deals with a toxin producing phytoplankton (tpp)-zooplankton interaction in spatial environment in thecontext of phytoplankton bloom. in the absence of diffusion the stability of the given system in terms of co-existence and hopf bifurcation has been discussed. after that tpp-zooplankton interaction is considered in spatiotemporal domain by assuming self diffusion in both popu...

We study the mechanism of development of superlattice Turing structures from photochemically generated hexagonal patterns of spots with wavelengths several times larger than the characteristic wavelength of the Turing patterns that spontaneously develop in the nonilluminated system. Comparison of the experiment with numerical simulations shows that interaction of the photochemical periodic forc...

Turing (1952) showed that under certain conditions, reaction and diffusion processes alone could lead to the symmetry-breaking instability (i.e., Turing instability) of a system (i.e., Turing system) from a homogeneous state to a stationary patterned state (Setayeshgar & Cross, 1999). Turing system can generate stationary patterns such as stripes and/or spots. Turing instability mechanism has p...