Related papers: Wavelength selection beyond Turing
We develop a theoretical model to investigate wave propagation in media with random time-varying properties, where temporal fluctuations lead to complex scattering dynamics. Focusing on the ensemble-averaged field, we derive an exact…
This is the second of two articles on the study of a particle system model that exhibits a Turing instability type effect. About the hydrodynamic quations obtained in \cite{CSL17a}, we find conditions under which Turing instability occurs…
This is the first of two articles on the study of a particle system model that exhibits a Turing instability type effect. The model is based on two discrete lines (or toruses) with Ising spins, that evolve according to a continuous time…
Ecological systems show a variety of characteristic patterns of biodiversity in space and time. It is a challenge for theory to find models that can reproduce and explain the observed patterns. Since the advent of island biogeography these…
The problem of morphogenesis and Turing instability are revisited from the point of view of dimensionality effects. First the linear analysis of a generic Turing model is elaborated to the case of multiple stationary states, which may lead…
Complex evolving systems such as the biosphere, ecosystems and societies exhibit sudden collapses, for reasons that are only partially understood. Here we study this phenomenon using a mathematical model of a system that evolves under…
We demonstrate that demographic noise can induce persistent spatial pattern formation and temporal oscillations in the Levin-Segel predator-prey model for plankton-herbivore population dynamics. Although the model exhibits a Turing…
Field patterns occur in space-time microstructures such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is…
Reaction-diffusion processes on networked systems have received mounting attention in the past two decades, and the corresponding theory of network dynamics has been continuously enriched with the advancement of network science. Recently,…
A feature common to many models of vegetation pattern formation in semi-arid ecosystems is a sequence of qualitatively different patterned states, "gaps -> labyrinth -> spots", that occurs as a parameter representing precipitation…
In the early Universe, large-scale flows were omnipresent, and the flow collisions produced sheets and filaments. This phenomenon occurs for both particle and wave dark matter. But for the latter, these sheets and filaments are the…
Nonlinear evolution of one-dimensional planar perturbations in an optically thin radiatively cooling medium in the long-wavelength limit is studied numerically. The accepted cooling function generates in thermal equilibrium a bistable…
The problem of pattern selection in absolutely unstable open flow systems is investigated by considering the example of Rayleigh-B\'{e}nard convection. The spatiotemporal structure of convection rolls propagating downstream in an externally…
Striped Turing patterns and solitary band and disk structures are constructed using a three-variable multiscale model with cubic nonlinearity and global control. The existence and stability conditions of regular structures are analysed…
The onset of convection in a rapidly rotating layer in which a thermal wind is present is studied. Diffusive effects are included. The main motivation is from convection in planetary interiors, where thermal winds are expected due to…
Piebaldism usually manifests as white areas of fur, hair or skin due to the absence of pigment-producing cells in those regions. The distribution of the white and colored zones does not follow the classical Turing patterns. Here we present…
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually…
Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty…
Spontaneous pattern formation in a variety of spatially extended nonlinear system always occurs through a modulation instability: homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…