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Our general aim is to give sufficient conditions for robustness behavior and convergence to the equilibrium point of linear time-varying fractional system's solutions. We approach this problem using as a framework a series of recent results…
We investigate the critical behavior of a reaction-diffusion system exhibiting a continuous absorbing-state phase transition. The reaction-diffusion system strictly conserves the total density of particles, represented as a non-diffusive…
The capacity to adapt can greatly influence the success of systems that need to compensate for damaged parts, learn how to achieve robust performance in new environments, or exploit novel opportunities that originate from new technological…
Recently, the problem of boundary stabilization for unstable linear constant-coefficient coupled reaction-diffusion systems was solved by means of the backstepping method. The extension of this result to systems with advection terms and…
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…
A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…
This article is concerned with the stability and long-time dynamics of structures arising from a structureless state. The paradigm is suggested by developmental biology, where morphogenesis is thought to result from a competition between…
Diffusion plays an important role in a wide variety of phenomena, from bacterial quorum sensing to the dynamics of traffic flow. While it generally tends to level out gradients and inhomogeneities, diffusion has nonetheless been shown to…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing…
Reaction-diffusion equations are widely used to describe a variety of phenomena such as pattern formation and front propagation in biological, chemical and physical systems. In the one-dimensional model with a balanced bistable reaction…
The random diffusion model is a continuum model for a conserved scalar density field driven by diffusive dynamics where the bare diffusion coefficient is density dependent. We generalize the model from one with a sharp wavenumber cutoff to…
Due to the diffusion of IoT, modern software systems are often thought to control and coordinate smart devices in order to manage assets and resources, and to guarantee efficient behaviours. For this class of systems, which interact…
In absence of advection, reaction-diffusion systems are able to organize into spatiotemporal patterns, in particular spiral and target waves. Whenever advection is present and can be parameterised in terms of effective or turbulent…
Evolving biomolecular networks have to combine the stability against perturbations with flexibility allowing their constituents to assume new roles in the cell. Gene duplication followed by functional divergence of associated proteins is a…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
Hyperbolic reaction-diffusion equations have recently attracted attention both for their application to a variety of biological and chemical phenomena, and for their distinct features in terms of propagation speed and novel instabilities…
We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
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…