Related papers: Turing instabilities on Cartesian product networks
The concept of cross diffusion is applied to some biological systems. The conditions for persistence and Turing instability in the presence of cross diffusion are derived. Many examples including: predator-prey, epidemics (with and without…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the…
Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, bio-fluids, atmosphere, oceans, and astrophysics. Despite exceptional theoretical,…
We develop exact field theoretic methods to treat turbulence when the effect of pressure is negligible. We find explicit forms of certain probability distributions, demonstrate that the breakdown of Galilean invariance is responsible for…
We describe the resulting spatiotemporal dynamics when a homogeneous equilibrium loses stability in a spatially extended system. More precisely, we consider reaction-diffusion systems, assuming only that the reaction kinetics undergo a…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
Striped patterns are known to bifurcate in reaction-diffusion systems with differential isotropic diffusions at a supercritical Turing instability. In this paper we study the impact of weak anisotropy by directional advection on the…
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…
The spontaneous emergence of ordered structures, known as Turing patterns, in complex networks is a phenomenon that holds potential applications across diverse scientific fields, including biology, chemistry, and physics. Here, we present a…
We investigate Turing pattern formation in a stochastic and spatially discretized version of a reaction diffusion advection (RDA) equation, which was previously introduced to model synaptogenesis in \textit{C. elegans}. The model describes…
We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random media. The random media contains point scatterers of density $\rho$ uniformly…
Turing patterns emerge from a spatially uniform state following a linear instability driven by diffusion. Features of the eventual pattern (stabilized by non-linearities) are already present in the initial unstable modes. On a uniform flat…
The process of stochastic Turing instability on a network is discussed for a specific case study, the stochastic Brusselator model. The system is shown to spontaneously differentiate into activator-rich and activator-poor nodes, outside the…
In confined plasmas, a localized fluctuation in a marginal or weakly damped region will propagate and generate an avalanche if it exceeds a threshold. In this letter, a new model for turbulence spreading based on subcritical instability in…
Sufficient conditions for the wave instability in general three-component reaction-diffusion systems are derived. These conditions are expressed in terms of the Jacobian matrix of the uniform steady state of the system, and enable us to…
The use of available disturbance predictions within a nominal model predictive control formulation is studied. The main challenge that arises is the loss of recursive feasibility and stability guarantees when a persistent disturbance is…
We study the phenomenon of entrainment in processor sharing networks, whereby, while individual network resources have sufficient capacity to met demand, the requirement for simultaneous availability of resources means that a network may…
Self-organization, the ability of a system of microscopically interacting entities to shape macroscopically ordered structures, is ubiquitous in Nature. Spatio-temporal patterns are abundantly observed in a large plethora of applications,…
In this article, we study the existence of insensitizing controls for a nonlinear reaction-diffusion equation with dynamic boundary conditions. Here, we have a partially unknown data of the system, and the problem consists in finding…
In this note, we propose a new idea by analyzing the basic disturbance equations, and give starting equations for understanding the instability phenomena of laminar flows and transition to turbulence. It is considered that there is an…