Related papers: Pattern alternations induced by nonlocal interacti…
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…
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with…
Deep neural networks have become increasingly of interest in dynamical system prediction, but out-of-distribution generalization and long-term stability still remains challenging. In this work, we treat the domain parameters of dynamical…
The employment of nonlocal PDE models to describe biological aggregation and other phenomena has gained considerable traction in recent years. For cell populations, these methods grant a means of accommodating essential elements such as…
How patterns and structures undergo symmetry breaking and self-organize within biological systems from initially homogeneous states is a key issue for biological development. The activator-inhibitor (AI) mechanism, derived from…
As proposed by Alan Turing in 1952 as a ubiquitous mechanism for nonequilibrium pattern formation, diffusional effects may destabilize uniform distributions of reacting chemical species and lead to both spatially and temporally…
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…
Both natural and synthetic chemical systems not only exhibit a range of non-trivial dynamics, but also transition between qualitatively different dynamical behaviours as environmental parameters change. Such transitions are called…
Abrupt transitions are ubiquitous in the dynamics of complex systems. Finding precursors, i.e. early indicators of their arrival, is fundamental in many areas of science ranging from electrical engineering to climate. However, obtaining…
A one-component bistable reaction-diffusion system with asymmetric nonlocal coup ling is derived as limiting case of a two-component activator-inhibitor reaction -diffusion model with differential advection. The effects of asymmetric…
Turing's theory of pattern formation is a universal model for self-organization, applicable to many systems in physics, chemistry and biology. Essential properties of a Turing system, such as the conditions for the existence of patterns and…
Pattern formation in reaction-diffusion systems where the diffusion terms correspond to a Sturm-Liouville problem are studied. These correspond to a problem where the diffusion coefficient depends on the spatial variable: $\nabla \cdot…
Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at…
We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion coefficients are large, this solution…
We estimate density of defects frozen into a biological Turing pattern which was turned on at a finite rate. A self-locking of gene expression in individual cells, which makes the Turing transition discontinuous, stabilizes the pattern…
For over 25 years it is known that the roll structure of electroconvection (EC) in the dielectric regime in planarly aligned nematic liquid crystals has, after a transition to defect chaos, the tendency to form chevron structures. We show,…
Spatio-temporal patterns emerging from an initial quiescent, uniform state is a phenomenon observed in many dynamical systems sustained far from thermodynamic equilibrium, the practical application of which has only recently begun to be…
Many decision making systems deployed in the real world are not static - a phenomenon known as model adaptation takes place over time. The need for transparency and interpretability of AI-based decision models is widely accepted and thus…
Artificial Neural Networks (ANNs) implement a specific form of multi-variate extrapolation and will generate an output for any input pattern, even when there is no similar training pattern. Extrapolations are not necessarily to be trusted,…
Pattern-forming nonequilibrium systems are ubiquitous in nature, from driven quantum matter and biological life forms to atmospheric and interstellar gases. Identifying universal aspects of their far-from-equilibrium dynamics and statistics…