Related papers: Interacting particles systems with delay and rando…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
The dynamics of an active walker in a harmonic potential is studied experimentally, numerically and theoretically. At odds with usual models of self-propelled particles, we identify two dynamical states for which the particle condensates at…
We consider two models of deterministic active particles in an external potential. In the limit where the speed of a particle is fixed, both models coincide and can be formulated as a Hamiltonian system, but only if the potential is…
A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology, ranging from the exchange of energy and matter with the surrounding environment to the change of particle number…
The evolution of particulate and multiphase systems can transition from dynamic regimes, governed by classical transport equations with well-defined damping coefficients, to anomalously slow relaxation described by rate equations when the…
A review of discrete quantum walk with two particle is given. The use of different states encountered in identical particle, and the idea of entanglement and superposition is explored to explored the interesting dynamics of two particle…
We introduce and analyse a continuum model for an interacting particle system of Vicsek type. The model is given by a non-linear kinetic partial differential equation (PDE) describing the time-evolution of the density $f_t$, in the single…
Time-delay systems are, in many ways, a natural set of dynamical systems for natural scientists to study because they form an interface between abstract mathematics and data. However, they are complicated because past states must be…
We explore theoretically the navigation of an active particle based on delayed feedback control. The delayed feedback enters in our expression for the particle orientation which, for an active particle, determines (up to noise) the…
We consider the dynamics of a collection of particles that interact pairwise and are restricted to move along the real line. Moreover, we focus on the situation in which particles undergo perfectly inelastic collisions when they collide.…
The finite duration of collisions appear as time-nonlocality in the kinetic equation. Analyzing the corresponding quantum kinetic equation for dense interacting Fermi systems a delay differential equation is obtained which combines time…
We investigate systems of self-propelled particles with alignment interaction. Compared to previous work, the force acting on the particles is not normalized and this modification gives rise to phase transitions from disordered states at…
The continuous limit of large systems of particles of finite size on the line is described. The particles are assumed to move freely and stick under collision, to form compound particles whose mass and size is the sum of the masses and…
Mobile microscopic bodies, such as motile cells, can be modelled phenomenologically as ``active particles'' which can move against external forces by depleting an internal energy depot. The microscopic mechanisms underlying such ``active''…
We prove the dynamical large deviations for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the so-called boundary driven process. The…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
We derive an analytic expression for the distribution of velocities of multiple interacting active particles which we test by numerical simulations. In clear contrast with equilibrium we find that the velocities are coupled to positions.…
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…
In this paper we provide an extension of the model discussed in [arXiv:1504.08283] describing two singularly interacting particles on the half-line. In this model, the particles are interacting only whenever at least one particle is…