Related papers: Non Standard Finite Difference Scheme for Mutualis…

Deterministic continuum models formulated in terms of non-local partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the…

Rare trajectories of stochastic systems are important to understand -- because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their…

Dynamical properties of numerically approximated discrete systems may become inconsistent with those of the corresponding continuous-time system. We present a qualitative analysis of the dynamical properties of two species Lotka-Volterra…

This paper introduces a class of non-linear and continuous-time opinion dynamics model with additive noise and state dependent interaction rates between agents. The model features interaction rates which are proportional to a negative power…

The importance of unspanned macroeconomic variables for Dynamic Term Structure Models has been intensively discussed in the literature. To our best knowledge the earlier studies considered only linear interactions between the economy and…

We present a novel multilevel Monte Carlo approach for estimating quantities of interest for stochastic partial differential equations (SPDEs). Drawing inspiration from [Giles and Szpruch: Antithetic multilevel Monte Carlo estimation for…

Mutualistic communities have an internal structure that makes them resilient to external per- turbations. Late research has focused on their stability and the topology of the relations between the different organisms to explain the reasons…

We discuss a discrete-time model for motion of substance in a channel of a network. For the case of stationary motion of the substance and for the case of time-independent values of the parameters of the model we obtain a new class of…

In the present work we extend the Bak-Sneppen model for biological evolution by introducing local interactions between species. This ``environmental'' perturbation can modify the intrinsic fitness of each element of the ecology, leading to…

This paper presents expression of mutual information that defines the information gain in planning of sensing resources, when the goal is to reduce the forecast uncertainty of some quantities of interest and the system dynamics is described…

Modeling the evolution of high-dimensional systems from limited snapshot observations at irregular time points poses a significant challenge in quantitative biology and related fields. Traditional approaches often rely on dimensionality…

The interaction between aphids, ants and ladybirds has been investigated from an ecological point of view since many decades, while there are no attempts to describe it from a mathematical point of view. This paper introduces a new…

I analyse a generalised Burger's equation to develop an accurate finite difference approximation to its dynamics. The analysis is based upon centre manifold theory so we are assured that the finite difference model accurately models the…

A wide range of non-equilibrium phenomena in nature involve non-reciprocal interactions. To understand the novel behaviors that can emerge in such systems, finding tractable models is essential. With this goal, we introduce a non-reciprocal…

Organisms shape their own environment, which in turn affects their survival. This feedback becomes especially important for communities containing a large number of species; however, few existing approaches allow studying this regime,…

Differential flatness serves as a powerful tool for controlling continuous time nonlinear systems in problems such as motion planning and trajectory tracking. A similar notion, called difference flatness, exists for discrete-time systems.…

We study quantum dynamics in the framework of repeated interactions between a system and a stream of identical probes. We present a coarse-grained master equation that captures the system's dynamics in the natural regime where interactions…

A continuum model for a population of self-propelled particles interacting through nematic alignment is derived from an individual-based model. The methodology consists of introducing a hydrodynamic scaling of the corresponding mean-field…

Collisions are an innate part of the function of many musical instruments. Due to the nonlinear nature of contact forces, special care has to be taken in the construction of numerical schemes for simulation and sound synthesis. Finite…

According to the dynamic van der Waals theory, we propose a thermodynamically consistent model for non-isothermal compressible two-phase flows with contact line motion. In this model, fluid temperature is treated as a primary variable,…