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Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
An evacuation process is simulated within the Social Force Model. Thousand pedestrians are leaving a room by one exit. We investigate the stationarity of the distribution of time lags between instants when two successive pedestrians cross…
We present numerical simulations of acoustic wave propagation in confined granular systems consisting of particles interacting with the three-dimensional Hertz-Mindlin force law. The response to a short mechanical excitation on one side of…
Saving energy and enhancing performance are secular preoccupations shared by both nature and human beings. In animal locomotion, flapping flyers or swimmers rely on the flexibility of their wings or body to passively increase their…
The flocking motion control is concerned with managing the possible conflicts between local and team objectives of multi-agent systems. The overall control process guides the agents while monitoring the flock-cohesiveness and localization.…
Flocking behavior has attracted considerable attention in multi-agent systems. The structure of flocking has been predominantly studied through the application of artificial potential fields coupled with velocity consensus. These…
In this paper we consider a model for the diffusion of a population in a strip-shaped field, where the growth of the species is governed by a Fisher-KPP equation and which is bounded on one side by a road where the species can have a…
We develop simple diffusion-advection models to estimate the average time it takes fish to reach one of the boundaries of an enclosure and the population distribution over time moving in the enclosure (such as a lake or slough). We start…
UAV collective motion has become a hot research topic in recent years. The realization of UAV collective motion, however, relied heavily on centralized control method and suffered from instability. Inspired by bird flocking theory, a…
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…
We formulate a kinetic theory of two species of hard spheres undergoing reactive collisions that convert chemical energy into kinetic energy. The model describes an active species interacting with a passive background, labeled as birds and…
There is now experimental evidence that nearest-neighbour interactions in flocks of birds are metric free, i.e. they have no characteristic interaction length scale. However, models that involve interactions between neighbours that are…
In this paper, we present a model describing the collective motion of birds. The model introduces spontaneous changes in direction which are initialized by few agents, here referred as leaders, whose influence act on their nearest…
The spontaneous organization of collective activities in animal groups and societies has attracted a considerable amount of attention over the last decade. This kind of coordination often permits group-living species to achieve collective…
The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a…
This paper investigates the dynamics of a reaction-diffusion system with two free boundaries, modeling the invasion of two cooperative species, where the free boundaries represent expanding fronts. We first analyze the long-term behavior of…
We treat a model of population dynamics in a periodic environment presenting a fast diffusion line. This phenomenon is modelled via a "road-field" system, which is a system of coupled reaction-diffusion equations set in domains of different…
Collective motion in animal groups, such as swarms of insects, flocks of birds, and schools of fish, are some of the most visually striking examples of emergent behavior. Empirical analysis of these behaviors in experiment or computational…
We discuss two cases that can be connected to the dynamics of interacting populations: (I.) density waves for the case or negligible random fluctuations of the populations densities, and (II.) probability distributions connected to the…
We propose a mathematical framework to systematically explore the propagation properties of a class of continuous in time nonlinear neural network models comprising a hierarchy of processing areas, mutually connected according to the…