Related papers: Modeling self-organized systems interacting with f…

Ecological systems comprise an astonishing diversity of species that cooperate or compete with each other forming complex mutual dependencies. The minimum requirements to maintain a large species diversity on long time scales are in general…

Criticality has been proposed as a key principle underlying complex behavior in biological and artificial systems; however, how criticality translates from individual dynamics to collective behavior remains unclear. We study this question…

We consider an ecological system governed by Lotka-Volterra dynamics and an example of an economic system as a mesomarket with perfect competition. We propose a mechanism for cooperative self-regulation that enables the system under…

In recent years modelling crowd and evacuation dynamics has become very important, with increasing huge numbers of people gathering around the world for many reasons and events. The fact that our global population grows dramatically every…

Structure, composition and stability of ecological populations are shaped by the inter- and intra-species interactions within these communities. It remains to be fully understood how the interplay of these interactions with other factors,…

Many systems in nature, from ferromagnets to flocks of birds, exhibit ordering phenomena on the large scale. In physical systems order is statistically robust for large enough dimensions, with relative fluctuations due to noise vanishing…

Self-organization of heterogeneous particle swarms is rich in its dynamics but hard to design in a traditional top-down manner, especially when many types of kinetically distinct particles are involved. In this chapter, we discuss how we…

Scientists investigate the dynamics of complex systems with quantitative models, employing them to synthesize knowledge, to explain observations, and to forecast future system behavior. Complete specification of systems is impossible, so…

A simple model economy with locally interacting producers and consumers is introduced. When driven by extremal dynamics, the model self-organizes {\em not} to an attractor state, but to an asymptote, on which the economy has a constant rate…

One of the fundamental problems in biology concerns the method by which a cluster of organisms can regulate the proportion of individuals that perform various roles or modes as if each individual knows a whole situation without a leader. A…

This work presents a microscopic model to describe pedestrian flows based on the social force theory. The aim of this study is twofold: (1) developing a realistic model that can be used as a tool for designing pedestrian-friendly…

Ecosystems are commonly conceptualized as networks of interacting species. However, partitioning natural diversity of organisms into discrete units is notoriously problematic, and mounting experimental evidence raises the intriguing…

In this paper, we begin by reviewing a certain number of mathematical challenges posed by the modelling of collective dynamics and self-organization. Then, we focus on two specific problems, first, the derivation of fluid equations from…

Interactions in natural communities can be highly heterogeneous, with any given species interacting appreciably with only some of the others, a situation commonly represented by sparse interaction networks. We study the consequences of…

Empirical evidence suggesting that living systems might operate in the vicinity of critical points, at the borderline between order and disorder, has proliferated in recent years, with examples ranging from spontaneous brain activity to…

This paper provides an overview and critical analysis on the modeling and applications of the dynamics of human crowds, where social interactions can have an important influence on the behavioral dynamics of the crowd viewed as a living,…

Starting from recent experimental observations of starlings and jackdaws, we propose a minimal agent-based mathematical model for bird flocks based on a system of second-order delayed stochastic differential equations with discontinuous…

Swarming is a conspicuous behavioural trait observed in bird flocks, fish shoals, insect swarms and mammal herds. It is thought to improve collective awareness and offer protection from predators. Many current models involve the hypothesis…

We undertake a systematic numerical exploration of self-organized states in a deterministic model of interacting self-propelled particles in two dimensions. In the process, we identify various types of collective motion, namely, disordered…

We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…