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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 simple model of co-evolution. In order to emphasise the effect of interaction between individuals the entire population is subjected to the same physical environment. Species are emergent structures and extinction, origination…
Over the last few decades, ecologists have come to appreciate that key ecological patterns, which describe ecological communities at relatively large spatial scales, are not only scale dependent, but also intimately intertwined. The…
A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation…
This paper presents a novel methodology for the direct numerical modeling and simulation of turbulent flows. The kinetic model equation is firstly extended to turbulent flow with the account of coupled evolution of kinetic, thermal, and…
A striking feature of the marine ecosystem is the regularity in its size spectrum: the abundance of organisms as a function of their weight approximately follows a power law over almost ten orders of magnitude. We interpret this as evidence…
What features characterise complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena[1-3]. Here we argue that slow,…
We consider several multiscale-in-time kinetic Monte Carlo models, in which some variables evolve on a fast time scale, while the others evolve on a slow time scale. In the first two models we consider, a particle evolves in a…
In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of…
In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic up in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a…
Animals chain movements into long-lived motor strategies, exhibiting variability across scales that reflects the interplay between internal states and environmental cues. To reveal structure in such variability, we build Markov models of…
Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the…
Eco-evolutionary dynamics, or eco-evolution for short, are thought to involve rapid demography (ecology) and equally rapid phenotypic changes (evolution) leading to novel, emergent system behaviours. This focus on contemporary dynamics is…
Planetary systems evolve over secular time scales. One of the key mechanisms that drive this evolution is tidal dissipation. Submitted to tides, stellar and planetary fluid layers do not behave like rocky ones. Indeed, they are the place of…
Dynamical tide consists of various waves that can resonate with orbital motion. We test this coupling of dynamical tide and orbital motion using a simple two-dimensional shallow water model, which can be applied to a rocky planet covered…
Scaling laws in ecology, intended both as functional relationships among ecologically-relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and…
The reaction-diffusion models have been extensively applied to explain the mechanism of pattern formations in early embryogenesis based on geometrically confined microtissues consisting of human pluripotent stem cells. Recently, mechanical…
Coral reefs are topologically complex environments with a large variation over small spatial-scales. The availability of high resolution data (metre-scale) to study these environments has increased rapidly such that many researchers are…
Clays control carbon, water and nutrient transport in the lithosphere, promote cloud formation5 and lubricate fault slip through interactions among hydrated mineral interfaces. Clay mineral properties are difficult to model because their…
The formation of dynamical patterns is one of the most striking features of nonequilibrium physical systems. Recent work has shown that such patterns arise generically from forces that violate Newton's third law, known as nonreciprocal…