Related papers: Capturing pattern bi-stability dynamics in delay-c…

A discrete delay is included to model the time between the capture of the prey and its conversion to viable biomass in the simplest classical Gause type predator-prey model that has equilibrium dynamics without delay. As the delay increases…

In this paper we consider a continuous-time anisotropic swarm model in $n$-dimensional space with an attraction/repulsion function and study its aggregation properties. It is shown that the swarm members will aggregate and eventually form a…

Swarm systems consist of large numbers of robots that collaborate autonomously. With an appropriate level of human control, swarm systems could be applied in a variety of contexts ranging from search-and-rescue situations to Cyber defence.…

Swarm dynamics is the study of collections of agents that interact with one another without central control. In natural systems, insects, birds, fish and other large mammals function in larger units to increase the overall fitness of the…

We investigate the effect of turning delays on the behaviour of groups of differential wheeled robots and show that the group-level behaviour can be described by a transport equation with a suitably incorporated delay. The results of our…

We introduce a stochastic agent-based model for the flocking dynamics of self-propelled particles that exhibit velocity-alignment interactions with neighbours within their field of view. The stochasticity in the dynamics of the model arises…

We discuss the collective dynamics of self-propelled particles with selective attraction and repulsion interactions. Each particle, or individual, may respond differently to its neighbors depending on the sign of their relative velocity.…

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…

We study the limits of linear modeling of swarm behavior by characterizing the inflection point beyond which linear models of swarm collective behavior break down. The problem we consider is a central place object gathering task. We design…

Interacting populations often create complicated spatiotemporal behavior, and understanding it is a basic problem in the dynamics of spatial systems. We study the two-species case by simulations of a host--parasitoid model. In the case of…

The biologically-inspired swarm paradigm is being used to design self-organizing systems of locally interacting artificial agents. A major difficulty in designing swarms with desired characteristics is understanding the causal relation…

Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When…

We investigate the collective motion of self-propelled agents in an environment filled with obstacles that are tethered to fixed positions via springs. The active particles are able to modify the environment by moving the obstacles through…

In swarm robotics, just as for an animal swarm in Nature, one of the aims is to reach and maintain a desired configuration. One of the possibilities for the team, to reach this aim, is to see what its neighbours are doing. This approach…

We construct two models of discrete-time replicator dynamics with time delay. In the social-type model, players imitate opponents taking into account average payoffs of games played some units of time ago. In the biological-type model, new…

In this paper we consider interacting particle systems which are frequently used to model collective behavior in animal swarms and other applications. We study the stability of orientationally aligned formations called flock solutions, one…

We study synchronization dynamics in populations of coupled phase oscillators with higher-order interactions and community structure. We find that the combination of these two properties gives rise to a number of states unsupported by…

Models of coordinated behavior of populations living in the same environment are introduced for the cases when they either compete with each other, or they both gain by mutual interactions, or finally when one hunts the other one. The…

Retardation between sensation and action is an inherent biological trait. Here we study its effect in the Vicsek model, which is a paradigmatic swarm model. We find that: (i) a discrete time delay in the orientational interactions…

Ultra-dense crowds, in which physical contact between people cannot be avoided, pose major safety concerns. Nevertheless, the underlying dynamics driving their collective behaviours remain poorly understood. Existing dense crowd models,…