Related papers: Competitively Coupled Maps and Spatial Pattern For…
We study the dynamics of one--dimensional discrete models of one--component active medium built up of spatially inhomogeneous chains of diffusively coupled piecewise linear maps. The nonhomogeneities (``defects'') are treated in terms of…
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…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
Structural causal models describe how the components of a robotic system interact. They provide both structural and functional information about the relationships that are present in the system. The structural information outlines the…
Regular vegetation patterns in semiarid ecosystems are believed to arise from the interplay between long-range competition and facilitation processes acting at smaller distances. We show that, under rather general conditions, long-range…
A simple and general formalism for mode coupling by a spatial, temporal or spatiotemporal perturbation in dispersive materials is developed. This formalism can be used for studying various linear and non-linear optical interactions…
This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the spatial epidemic model by Turing mechanisms. In particular, we present theoretical analysis to results of the numerical…
This article is concerned with the stability and long-time dynamics of structures arising from a structureless state. The paradigm is suggested by developmental biology, where morphogenesis is thought to result from a competition between…
Pattern formation in clouds is a well-known feature, which can be observed almost every day. However, the guiding processes for structure formation are mostly unknown, and also theoretical investigations of cloud patterns are quite rare.…
We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing…
In this paper we investigate the ability of some recently introduced discrete kinetic models of vehicular traffic to catch, in their large time behavior, typical features of theoretical fundamental diagrams. Specifically, we address the…
Enhancement of the predictive power and robustness of nonlinear population dynamics models allows ecologists to make more reliable forecasts about species' long term survival. However, the limited availability of detailed ecological data,…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
Many climate subsystems are thought to be susceptible to tipping - and some might be close to a tipping point. The general belief and intuition, based on simple conceptual models of tipping elements, is that tipping leads to reorganization…
As a model of temporally evolving networks, we consider a globally coupled logistic map with variable connection weights. The model exhibits self-organization of network structure, reflected by the collective behavior of units. Structural…
Patterns are ubiquitous in nature, but how they form is often unclear. Turing developed a seminal theory to explain patterns based on reactions that counteract the equalizing tendency of diffusion. These reactions require continuous energy…
A model for a monolayer of two types of particles spontaneously forming ordered patterns is studied by a mesoscopic theory and by MC simulations. We assume hard-cores of the same size for both components, short-range attraction long-range…
We present a simple model based on a reaction-diffusion equation to explain pattern formation in a multicellular bacterium (Streptomyces). We assume competition for resources as the basic mechanism that leads to pattern formation; in…
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when…
Understanding the pattern formation in communities has been at the center of attention in various fields. Here we introduce a novel model, called an "information-particle model," which is based on the reaction-diffusion model and the…