Related papers: Turing instabilities are not enough to ensure patt…
To investigate novel aspects of pattern formation in spin systems, we use a mapping between reactive concentrations in a reaction-diffusion system and spin orientations in a dynamic multiple-spin Ising model. While pattern formation in…
Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…
The Turing instability paradigm is revisited in the context of a multispecies diffusion scheme derived from a self-consistent microscopic formulation. The analysis is developed with reference to the case of two species. These latter share…
Pattern formation in clouds is a well-known feature, which can be observed almost every day. However, the guiding processes for structure formation are mostly unknown, and also theoretical investigations of cloud patterns are quite rare.…
A ternary reaction-diffusion model for early HIV infection dynamics, incorporating logistic growth of target cells, is introduced. According to in vitro and in vivo studies, random movement of target cells, infected cells, and virions and a…
Spatial patterns arising spontaneously due to internal processes are ubiquitous in nature, varying from regular patterns of dryland vegetation to complex structures of bacterial colonies. Many of these patterns can be explained in the…
We consider a two dimensional Turing like system with two diffusing species which interact with each other. Considering the species to be charged, we include the effect of an electric field along a given direction which can lead to a drift…
Reaction-diffusion processes on networked systems have received mounting attention in the past two decades, and the corresponding theory of network dynamics has been continuously enriched with the advancement of network science. Recently,…
We analyzed conditions for Hopf and Turing instabilities to occur in two-component fractional reaction-diffusion systems. We showed that the eigenvalue spectrum and fractional derivative order mainly determine the type of instability and…
Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…
The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…
The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as small parameter in the expansion and the unperturbed state…
Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the…
We study a p-adic reaction-diffusion system and the associated Turing patterns. We establish an instability criteria and show that the Turing patterns are not classical patterns consisting of alternating domains. Instead of this, a Turing…
It is well known that simple reaction-diffusion systems can display very rich pattern formation behavior. Here we have studied two examples of such systems in three dimensions. First we investigate the morphology and stability of a generic…
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…
Turing patterns, arising from the interplay between competing species of diffusive particles, has long been an important concept for describing non-equilibrium self-organization in nature, and has been extensively investigated in many…
Nature is intrinsically heterogeneous, and remarkable phenomena can only be observed in the presence of intrinsically nonlinear heterogeneities. Spontaneous pattern formation in nature has fascinated humankind for centuries, and the…
We consider a reaction-diffusion system undergoing Turing instability and augment it by an additional unilateral source term. We investigate its influence on the Turing instability and on the character of resulting patterns. The nonsmooth…
Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights,…