Related papers: Flocking in the Cucker-Smale model with self-delay…
This article proposes a non-autonomous mathematical model with delay for confrontation between two countries, and examines the stability of its equilibrium state. Our criteria for stability take into account the influence of the factor of…
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.
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…
We show that a cumulative action of noise and delayed feedback on an excitable theta-neuron leads to rather coherent stochastic bursting. An idealized point process, valid if the characteristic time scales in the problem are well-separated,…
The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…
The paper deals with a multiple species Lotka-Volterra model with infinite distributed delays and feedback controls, for which we assume a weak form of diagonal dominance of the instantaneous negative intra-specific terms over the infinite…
We establish necessary and sufficient conditions for convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. We show that this convergence is equivalent to asymptotic independence…
We consider three classes of linear non-symmetric Fokker-Planck equations having a unique steady state and establish exponential convergence of solutions towards the steady state with explicit (estimates of) decay rates. First,…
We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one…
Robots sometimes have to work together with a mixture of partially-aligned or conflicting goals. Flocking - coordinated motion through cohesion, alignment, and separation - traditionally assumes uniform desired inter-agent distances. Many…
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…
There are several results on the stability of nonlinear positive systems in the presence of time delays. However, most of them assume that the delays are constant. This paper considers time-varying, possibly unbounded, delays and…
A kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into…
In this paper we study well-posedness and asymptotic stability for a class of nonlinear second-order evolution equations with intermittent delay damping. More precisely, a delay feedback and an undelayed one act alternately in time. We show…
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…
In this paper we study asymptotic behaviour of a growth process generated by a semi-deterministic variant of cooperative sequential adsorption model (CSA). This model can also be viewed as a particular queueing system with local…
We address the design of decentralized feedback control laws inducing consensus and prescribed spatial patterns over a singular interacting particle system of Cucker-Smale type. The control design consists of a feedback term regulating the…
In this paper, we consider a multi-agent system consisting of mobile agents with second-order dynamics. The communication network is determined by the so-called topological interaction rule: agents interact with a fixed number of their…
We investigate asymptotic decay phenomenon towards the nonequilibrium steady state of the thermal diffusion in the presence of a tilted periodic potential. The parameter dependence of the decay rate is revealed by investigating the…
Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…