Related papers: On Cucker-Smale model with noise and delay
Animals living in groups make movement decisions that depend, among other factors, on social interactions with other group members. Our present understanding of social rules in animal collectives is mainly based on empirical fits to…
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…
For the discrete Cucker-Smale's flocking model with a singular communication weight $\psi(s) = s^{-\alpha}$, with $0<\alpha<1/2$ , we prove that the velocity component of certain type of weak solutions is absolutly continuous. This result…
We present an emergent stochastic flocking dynamics of the Cucker-Smale (CS) ensemble under randomly switching topologies. The evolution of the CS ensemble with randomly switching topologies involves two random components (switching times…
Animals having a trend to align their velocities to an average of their neighbors' may flock as illustrated by the Vicsek model and its variants. If, in addition, they feel a systematic contrarian trend, the result may be a time periodic…
We present a stochastic version of the Cucker-Smale flocking dynamics based on a markovian $N$-particle system of pair interactions with unbounded and, in general, non-Lipschitz continuous interaction potential. We establish the infinite…
A new nudging method for data assimilation, delay-coordinate nudging, is presented. Delay-coordinate nudging makes explicit use of present and past observations in the formulation of the forcing driving the model evolution at each…
A class of stochastic individual-based models, written in terms of coupled velocity jump processes, is presented and analysed. This modelling approach incorporates recent experimental findings on behaviour of locusts. It exhibits nontrivial…
Collective movement is observed widely in nature, where individuals interact locally to produce globally ordered, coherent motion. In typical models of collective motion, each individual takes the average direction of multiple neighbors,…
We show that peculiar collective dynamics called slow switching arises in a population of leaky integrate-and-fire oscillators with delayed, all-to-all pulse-couplings. By considering the stability of cluster states and symmetry possessed…
We develop a generating functional description of the dynamics of non-Markovian individual-based systems, in which delay reactions can be terminated before completion. This generalises previous work in which a path-integral approach was…
We study a model of binary decisions in a fully connected network of interacting agents. Individual decisions are determined by social influence, coming from direct interactions with neighbours, and a group level pressure that accounts for…
We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
We consider the kinetic Cucker-Smale model with local alignment as a mesoscopic description for the flocking dynamics. The local alignment was first proposed by Karper, Mellet and Trivisa \cite{K-M-T-3}, as a singular limit of a normalized…
We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common…
We propose that feedback-delayed manual tracking performance is limited by fundamental constraints imposed by the physics of negative group delay. To test this hypothesis, the results of an experiment in which subjects demonstrate both…
We perform a numerical analysis of a recent introduced model for describing collective movement in alarmed animals groups. This model, derived from a position-based interaction and a limited attention field, displays a non-equilibrium phase…
In this paper we propose and study a hybrid discrete in continuous mathematical model of collective motion under alignment and chemotaxis effect. Starting from the paper by Di Costanzo et al (2015a), in which the Cucker-Smale model (Cucker…