相关论文: Asymptotic flocking for the Cucker-Smale model wit…
We investigate the effects of delayed interactions on the stationary distribution of the noisy voter model. We assume that the delayed interactions occur through the periodic polling mechanism and replace the original instantaneous…
Collective motion - or flocking - is an emergent phenomena that underlies many biological processes of relevance, from cellular migrations to animal groups movement. In this work, we derive scaling relations for the fluctuations of the mean…
Collective dynamics of many interacting particles have been widely studied because of a wealth of their behavioral patterns quite different from the individual traits. A selective way of birds that reacts to their neighbors is one of the…
Collective behaviors such as swarming and flocking emerge from simple, decentralized interactions in biological systems. Existing models, such as Vicsek and Cucker-Smale, lack collision avoidance, whereas the Olfati-Saber model imposes…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…
We investigate the asymptotic behaviour of solutions of a class of nonlocal Fokker--Planck equations defined by nonsingular, heavy-tailed convolution kernels and characterised by a scaling parameter $\e\in(0,1]$ and a fractional index…
We have identified the existence of globally clustered chimera states in delay coupled oscillator populations and find that these states can breathe periodically, aperiodically and become unstable depending upon the value of coupling delay.…
In this paper, we study the behavior of systems of individuals in confined environments that are driven by laws of self-organization. We propose that, under certain conditions, the long-term behavior of such systems will be global…
This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is…
This paper investigates asymptotic behavior of a stochastic SIR epidemic model, which is a system with degenerate diffusion. It gives sufficient conditions that are very close to the necessary conditions for the permanence. In addition,…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
Conditions are given under which the empirical copula process associated with a random sample from a bivariate continuous distribution has a smaller asymptotic covariance function than the standard empirical process based on observations…
In this article, a new mathematical model of human population growth as an autonomous non-Markov queuing system with an unlimited number of servers and two types of applications is proposed. The research of this system was carried out a…
We generalize the elementary mechanism of sampling with replacement $N$ times from a weighted population of size $N$, by introducing auxiliary variables and constraints on conditional independence characterised by modular congruence…
The Cucker-Smale flocking model belongs to a wide class of kinetic models that describe a collective motion of interacting particles that exhibit some specific tendency e.g. to aggregate, flock or disperse. The paper examines the kinetic…
We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the…
This paper studies a flocking model in which the interaction between agents is described by a general local nonlinear function depending on the distance between agents.
Flocking refers to collective behavior of a large number of interacting entities, where the interactions between discrete individuals produce collective motion on the large scale. We employ an agent-based model to describe the microscopic…
Swarms of large numbers of agents appear in many biological and engineering fields. Dynamic bi-stability of co-existing spatio-temporal patterns has been observed in many models of large population swarms. However, many reduced models for…
This paper considers a general class of nonparametric time series regression models where the regression function can be time-dependent. We establish an asymptotic theory for estimates of the time-varying regression functions. For this…