Related papers: Dynamics of spatial logistic model: finite systems
The stochastic differential equations for a model of dissipative particle dynamics with both total energy and total momentum conservation in the particle-particle interactions are presented. The corresponding Fokker-Planck equation for the…
In this report we summarize a few methods for solving the stochastic differential equations (SDE) and the corresponding Fokker-Planck equations describing the Gompertz and logistic random dynamics. It is shown that the solutions of the…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might…
To describe population dynamics, it is crucial to take into account jointly evolution mechanisms and spatial motion. However, the models which include these both aspects, are not still well-understood. Can we extend the existing results on…
We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains…
We construct birth-and-death Markov evolution of states(distributions) of point particle systems in $\mathbb{R}^d$. In this evolution, particles reproduce themselves at distant points (disperse) and die under the influence of each other…
We review recent results on the dynamics of continuous collapse models (or equivalently continuous measurement models) on finite dimensional Hilbert spaces. We mainly study the pure collapse dynamics, and the competition between collapse…
Many climate subsystems are thought to be susceptible to tipping - and some might be close to a tipping point. The general belief and intuition, based on simple conceptual models of tipping elements, is that tipping leads to reorganization…
Persistence in spatially extended dynamical systems (like coarsening systems and other nonequilibrium systems) is reviewed. We discuss, in particular, the spatial correlations in the persistent regions and their evolution in time in these…
In this article, we present an Unfitted Space-Time Finite Element method for the scalar transport equation posed on moving domains. We consider the case of the domain boundary being transported by the same velocity field as the scalar…
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…
We consider the extension of a tractable NEG model with a quasi-linear log utility to continuous space, and investigate the behavior of its solution mathematically. The model is a system of nonlinear integral and differential equations…
This report presents some fundamental mathematical results towards elucidating the information-geometric underpinnings of evolutionary modelling schemes for (quasi-)stationary discrete stochastic processes. The model class under…
We study a discrete time spatial branching system on $\mathbb{Z}^d$ with logistic-type local regulation at each deme depending on a weighted average of the population in neighboring demes. We show that the system survives for all time with…
We study well-posedness and long time behavior of the nonlinear Vlasov-Poisson- Fokker-Planck system with an external confining potential. The system describes the time evolution of particles (e.g.$\,\,$in a plasma) undergoing diffusion,…
The study of emergent behavior of swarms is of great interest for applied sciences. One of the most fundamental questions for self-organizing swarms is whether the swarms disperse or remain in a spatially cohesive configuration. In the…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
The dynamics of an infinite system of point particles in $\mathbb{R}^d$, which hop and interact with each other, is described at both micro- and mesoscopic levels. The states of the system are probability measures on the space of…
The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion dynamics of self-gravitating particles within the Einstein theory of general relativity. We study the Cauchy problem for spatially homogeneous and isotropic solutions…