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We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…
Molecules in dense environments, such as biological cells, are subjected to forces that fluctuate both in time and in space. While spatial fluctuations are captured by Lifson-Jackson-Zwanzig's model of "diffusion in a rough potential", and…
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…
Although the pattern formation on polymer gels has been considered as a result of the mechanical instability due to the volume phase transition, we found a macroscopic surface pattern formation not caused by the mechanical instability. It…
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish criteria…
Reaction-diffusion-advection media on semi-infinite domains are important in chemical, biological and ecological applications, yet remain a challenge for pattern formation theory. To demonstrate the rich emergence of nonlinear traveling…
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…
Diffusion within porous media, such as biological tissues, exhibits departures from conventional Fick's laws, which could result in space-fractional diffusion. The paper considers a reaction-diffusion system with two spatial compartments --…
The reversible reactions like A+B <-> C in the many-component diffusive system affect the diffusive properties of the constituents. The effective conjugation of irreversible processes of different dimensionality takes place due to the…
Morphogenesis is the ensemble of processes that determines form, shape and patterns in organisms. Based on a reaction-diffusion theoretical setting and some prototype reaction schemes, we make a review of the models and experiments that…
Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarisation. We develop…
Backpropagation-optimized artificial neural networks, while precise, lack robustness, leading to unforeseen behaviors that affect their safety. Biological neural systems do solve some of these issues already. Unlike artificial models,…
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…
This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…
Spreading processes on top of active dynamics provide a novel theoretical framework for capturing emerging collective behavior in living systems. I consider run-and-tumble dynamics coupled with coagulation/decoagulation reactions that lead…
Large time dynamics of reaction-diffusion systems modeling some irreversible reaction networks are investigated. Depending on initial masses, these networks possibly possess boundary equilibria, where some of the chemical concentrations are…
It has recently been shown that structural conditions on the reaction network, rather than a 'fine-tuning' of system parameters, often suffice to impart 'absolute concentration robustness' on a wide class of biologically relevant,…
We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis in the right-hand side. The input of hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic…
Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology,…
A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…