At the molecular level, the evolution of life is driven by the generation and diversification of
adaptation mechanisms. A universal description of adaptation-capable chemical reaction …

Nature is a blossoming of regular structures, signature of self-organization of the underlying
microscopic interacting agents. Turing theory of pattern formation is one of the most studied …

This is a book about 'Neurodynamics'. What we mean is that this is a book about how ideas
from dynamical systems theory have been developed and employed in recent years to give …

Necessary and sufficient conditions are provided for a diffusion-driven instability of a stable
equilibrium of a reaction–diffusion system with n components and diagonal diffusion matrix …

A wide variety of stationary or moving spatially localized structures is present in evolution
problems on unbounded domains, governed by higher-than-second-order reversible spatial …

In certain biological contexts, such as the plumage patterns of birds and stripes on certain
species of fishes, pattern formation takes place behind a so-called “wave of competency” …

Turing instability is a fundamental mechanism of nonequilibrium self-organization. However,
despite the universality of its essential mechanism, Turing instability has thus far been …

A wave bifurcation is the counterpart to a Turing instability in reaction–diffusion systems, but
where the critical wavenumber corresponds to a pure imaginary pair rather than a zero …

We study pattern formation in class of a large-dimensional neural networks posed on
random graphs and subject to spatio-temporal stochastic forcing. Under generic conditions …

Precise conditions are provided for the existence and criticality of Turing bifurcations in a
general class of activator-inhibitor reaction-diffusion equations on a one-dimensional infinite …