Related papers: On Cucker-Smale model with noise and delay
We introduce a multi-dimensional variant of the kinetic Cucker-Smale model with singular and matrix-valued communication weight, which reduces to the singular kinetic Cucker-Smale equation in the one-dimensional case. We propose an…
The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable L\'evy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time…
This paper focuses on the dynamical properties of delayed complex balanced systems. We first study the relationship between the stoichiometric compatibility classes of delayed and non-delayed systems. Using this relation we give another way…
Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…
Hidden Markov models (HMMs) are commonly used to model animal movement data and infer aspects of animal behavior. An HMM assumes that each data point from a time series of observations stems from one of $N$ possible states. The states are…
Quasi steady state assumptions are often used to simplify complex systems of ordinary differential equations in modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original…
In this work, we examine a kinetic framework for modeling the time evolution of size distribution densities of two populations governed by predator-prey interactions. The model builds upon the classical Boltzmann-type equations, where the…
The paper examines the problems related to the well-posedness of the Cucker-Smale model with communication restricted to the $q$-closest neighbors, known also as the Cucker-Dong model. With agents oscillating on the boundary of different…
Motivated by applications in movement ecology, in this paper I propose a new class of integrated continuous-time hidden Markov models in which each observation depends on the underlying state of the process over the whole interval since the…
By introducing a predictive mechanism with small-world connections, we propose a new motion protocol for self-driven flocks. The small-world connections are implemented by randomly adding long-range interactions from the leader to a few…
We study finite-time flocking for an infinite set of Cucker-Smale particles with sublinear velocity coupling under fixed and switching sender networks. For this, we use a component-wise diameter framework and exploit sub-linear dissipation…
Biological motor control provides highly effective solutions to difficult control problems in spite of the complexity of the plant and the significant delays in sensory feedback . Such delays are expected to lead to non trivial stability…
In this paper we investigate a structured population model with distributed delay. Our model incorporates two different types of nonlinearities. Specifically we assume that individual growth and mortality are affected by scramble…
This paper proposes a hierarchical spatial-temporal model for modelling the spectrograms of animal calls. The motivation stems from analyzing recordings of the so-called grunt calls emitted by various lemur species. Our goal is to identify…
We propose an alternative delayed population growth difference equation model based on a modification of the Beverton-Holt recurrence, assuming a delay only in the growth contribution that takes into account that those individuals that die…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
The present paper addresses the swing equation with additional delayed damping as an example for pendulum-like systems. In this context, it is proved that recurring sub- and supercritical Hopf bifurcations occur if time delay is increased.…
We propose a mathematical model, namely a reaction-diffusion system, to describe social behaviour of cockroaches. An essential new aspect in our model is that the dispersion behaviour due to overcrowding effect is taken into account {as a…
Fish, birds, insects and robots frequently swim or fly in groups. During their 3 dimensional collective motion, these agents do not stop, they avoid collisions by strong short-range repulsion, and achieve group cohesion by weak long-range…
This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential…