相关论文: Asymptotic flocking for the Cucker-Smale model wit…

In this paper, we deal with first and second-order alignment models with non-universal interaction, time delay and possible lack of connection between the agents. More precisely, we analyze the situation in which the system's agents do not…

We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…

We examine a class of stochastic differential inclusions involving multiscale effects designed to solve a class of generalized variational inequalities. This class of problems contains constrained convex non-smooth optimization problems,…

To study population dynamics, ecologists and wildlife biologists use relative abundance data, which are often subject to temporal preferential sampling. Temporal preferential sampling occurs when sampling effort varies across time. To…

We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use $\theta$-weak dependence to establish laws of large numbers and central limit type…

We consider a general model of self-propelling particles interacting through a pairwise attractive force in the presence of noise and communication time delay. Previous work by Erdmann, et al. [Phys. Rev. E {\bf 71}, 051904 (2205)] has…

We derive an explicit form for the Cucker-Smale (CS) model on the special orthogonal group $\mathrm{SO}(3)$ by identifying closed form expressions for geometric quantities such as covariant derivative and parallel transport in exponential…

The relationship between a time-dependent covariate and survival times is usually evaluated via the Cox model. Time-dependent covariates are generally available as longitudinal data collected regularly during the course of the study. A…

We consider the model selection problem for a large class of time series models, including, multivariate count processes, causal processes with exogenous covariates. A procedure based on a general penalized contrast is proposed. Some…

We consider a compressible Euler system with singular velocity alignment, known as the Euler-alignment system, describing the flocking behaviors of large animal groups. We establish a local well-posedness theory for the system, as well as a…

In this article, we consider flexible seasonal time series models which consist of a common trend function over periods and additive individual trend (seasonal effect) functions. The consistency and asymptotic normality of the local linear…

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…

It is known from both theory and experiments that introducing time delays into the communication network of mobile-agent swarms produces coherent rotational patterns. Often such spatio-temporal rotations can be bistable with other swarming…

We study a discrete time multitype branching random walk on a finite space with finite set of types. Particles follow a Markov chain on the spatial space whereas offspring distributions are given by a random field that is fixed throughout…

Most data processing techniques, applied to biomedical and sociological time series, are only valid for random fluctuations that are stationary in time. Unfortunately, these data are often non stationary and the use of techniques of…

Living many-body systems often exhibit scale-free collective behavior reminiscent of thermal critical phenomena. But their mutual interactions are inevitably retarded due to information processing and delayed actuation. We numerically…

In this paper, we consider a type of continuous time random walk model where the jump length is correlated with the waiting time. The asymptotic behaviors of the coupled jump probability density function in the Fourier-Laplace domain are…

In this paper, we investigate the convergence of asymptotic systems in non-autonomous Cohen--Grossberg neural network models, which include both infinite discrete time-varying and distributed delays. We derive stability results under…

The aim of this paper is to provide a systematic overview of results on asymptotic consensus for the Hegselmann-Krause-type model with delay and discuss the corresponding analytical tools. We explain that two types (sources) of delay -…

We analyze the dynamics of models of warm inflation with general dissipative effects. We consider phenomenological terms both for the inflaton decay rate and for viscous effects within matter. We provide a classification of the asymptotic…