相关论文: Transient Instability and Patterns of Reactivity i…

A class of hyperbolic reaction--diffusion models with cross-diffusion is derived within the context of Extended Thermodynamics. Linear stability analysis is performed to study the nature of the equilibrium states against uniform and…

We study pattern formation in a reaction-diffusion system for a benthic bacteria-nutrient model in a marine sediment, which originally contains some spatially varying coefficients and with these shows some layering of patterns. Using the…

The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…

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…

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.…

We report a new mechanism of pattern formation in growing bistable systems coupled indirectly. A modified Fujita et. al. model is studied as an example of a reaction-diffusion system of nondiffusive activator and inhibitor molecules…

Models based on surfactant driven instabilities have been employed to describe pattern formation by swarming bacteria. However, by definition, such models cannot account for the effect of bacterial sensing and decision making. Here we…

Motivated by numerical simulations showing the emergence of either periodic or irregular patterns, we explore a mechanism of pattern formation arising in the processes described by a system of a single reaction-diffusion equation coupled…

This paper proposes a control theoretic framework to model and analyze the self-organized pattern formation of molecular concentrations in biomolecular communication networks, emerging applications in synthetic biology. In biomolecular…

Confirming Turing's theory of morphogens in developmental processes is challenging, and synthetic biology has opened new avenues for testing Turing's predictions. Synthetic mammalian pattern formation has been recently achieved through a…

Pattern formation analysis of eco-epidemiological models with cannibalism and disease has been less explored in the literature. Therefore, motivated by this, we have proposed a diffusive eco-epidemiological model and performed pattern…

Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…

The aim of this work is to study the effect of diffusion on the stability of the equilibria in a general two-components reaction-diffusion system with Neumann boundary conditions in the space of continuous functions. As by product, we…

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 is a paradigmatic route to patterns formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a…

In this work, we focus on an autocatalytic reaction-diffusion model and carry out multiple scale weakly nonlinear analysis. A cubic and a quadratic autocatalytic reaction system is analysed. We develop a framework to identify the critical…

Analytically tracking patterns emerging from a small amplitude Turing instability to large amplitude remains a challenge as no general theory exists. In this paper, we consider a three component reaction-diffusion system with one of its…

This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusion-driven instability (DDI) and establishing the existence of…

Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and…

We propose a continuum model for pattern formation, based on the multiphase model framework, to explore in vitro cell patterning within an extracellular matrix. We demonstrate that, within this framework, chemotaxis-driven cell migration…