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We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
We study the $\beta$ analogue of the nonintersecting Poisson random walks. We derive a stochastic differential equation of the Stieltjes transform of the empirical measure process, which can be viewed as a dynamical version of the…
This article is on collective phenomena in pedestrian dynamics during the assembling and dispersal phases of gatherings. To date pedestrian dynamics have been primarily studied in the natural and engineering sciences. Pedestrians are…
Discrete time random walks, in which a step of random sign but constant length $\delta x$ is performed after each time interval $\delta t$, are widely used models for stochastic processes. In the case of a correlated random walk, the next…
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…
Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense…
This paper presents a new approach to behavioral-social dynamics of human crowds. First order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional…
With the aim of understanding the emergence of collective motion from local interactions of organisms in a "noisy" environment, we study biologically inspired, inherently non-equilibrium models consisting of self-propelled particles. In…
We propose a novel computational method to extract information about interactions among individuals with different behavioral states in a biological collective from ordinary video recordings. Assuming that individuals are acting as finite…
We present a comprehensive study of Vicsek-style self-propelled particle models in two and three space dimensions. The onset of collective motion in such stochastic models with only local alignment interactions is studied in detail and…
We propose a simple adaptive-network model describing recent swarming experiments. Exploiting an analogy with human decision making, we capture the dynamics of the model by a low-dimensional system of equations permitting analytical…
Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random…
Legged locomotion involves various gaits. It has been observed that fast running insects (cockroaches) employ a tripod gait with three legs lifted off the ground simultaneously in swing, while slow walking insects (stick insects) use a…
The interaction of the actin cytoskeleton with cell-substrate adhesions is necessary for cell migration. While the trajectories of motile cells have a stochastic character, investigations of cell motility mechanisms rarely elaborate on the…
We study a simple sandpile model of active-absorbing state transitions in which a particle can hop out of a site only if the number of particles at that site is above a certain threshold. We show that the active phase has product measure…
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…
In animal groups, individual decisions are best characterised by probabilistic rules. Furthermore, animals of many species live in small groups. Probabilistic interactions among small numbers of individuals lead to a so called intrinsic…
The internal behaviour of a population is an important feature to take account of when modelling their dynamics. In line with kin selection theory, many social species tend to cluster into distinct groups in order to enhance their overall…
Local interactions drive emergent collective behavior, which pervades biological and social complex systems. But uncovering the interactions that produce a desired behavior remains a core challenge. In this paper, we present EvoSOPS, an…
The giant single-celled slime mould Physarum polycephalum exhibits complex morphological adaptation and amoeboid movement as it forages for food and may be seen as a minimal example of complex robotic behaviour. Swarm computation has…