Related papers: Pattern formation in individual-based systems with…
Structured models, such as PDEs structured by age or phenotype, provide a setting to study pattern formation in heterogeneous populations. Classical tools to quantify the emergence of patterns, such as linear and weakly nonlinear analyses,…
We study erratically moving spatial structures that are found in a driven interface in a random medium at the depinning threshold. We introduce a bond-disordered variant of the Sneppen model and study the effect of extremal dynamics on the…
Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issue of understanding the emergence of neural patterns by…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that…
We propose a new non-equilibrium model for spatial pattern formation on the basis of local information transfer. Unlike standard models of pattern formation it is not based on the Turing instability. Information is transmitted through the…
When applying two counter-propagating laser beams to a cold cloud of Rubidium atoms, we observe the spontaneous formation of intensity patterns associated with a spatial structuration of the atomic spins. We study the average number of…
Pattern formation is a visual understanding of the dynamics of complex systems. Patterns arise in many ways, such as the segmentation of animals, bacterial colonies during growth, vegetation, chemical reactions, etc. In most cases, the…
When a collection of phenotypically diverse organisms compete with each other for limited resources, with competition being strongest amongst the most similar, the population can evolve into tightly localised clusters. This process can be…
We introduce and analyse an individual-based evolutionary model, in which a population of genetically diverse organisms compete with each other for limited resources. Through theoretical analysis and stochastic simulations, we show that the…
This paper investigates the conditions for the formation of local bumps in the activity of binary attractor neural networks with spatially dependent connectivity. We show that these formations are observed when asymmetry between the…
Neural networks acquire structured representations at specific moments during training, yet identifying these transitions typically relies on retrospective, label-dependent metrics. We introduce a bifurcation theory of representation…
We study the effects of noise on the dynamics of a system of coupled self-propelling particles in the case where the coupling is time-delayed, and the delays are discrete and randomly generated. Previous work has demonstrated that the…
Biological pattern formation is one of the most intriguing phenomena in nature. Simplest examples of such patterns are represented by travelling waves and stationary periodic patterns which occur during various biological processes…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
We introduce and analyze a voter-type model on a two-layer multiplex network, where the presence of a state on one layer acts as a catalyst or inhibitor to the propagation of that state on the other layer. Despite the model's simplicity,…
In models with dynamical electroweak symmetry breaking, this breaking is normally communicated to quarks and leptons by a set of vector bosons with masses generated via sequential breaking of a larger gauge symmetry. In reasonably…
We study the mechanisms of pattern formation for vegetation dynamics in water-limited regions. Our analysis is based on a set of two partial differential equations (PDEs) of reaction-diffusion type for the biomass and water and one ordinary…
Robust statistical features have emerged from the microscopic analysis of dense pedestrian flows through a bottleneck, notably with respect to the time gaps between successive passages. We pinpoint the mechanisms at the origin of these…
The characteristic size for spatial structure, that emerges when the bifurcation parameter in model partial differential equations is slowly increased through its critical value, depends logarithmically on the size of added noise. Numerics…