相关论文: A Stochastic Differential Equation Model for Preda…

We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…

The model of competition between densities of two different species, called predator and prey, is studied on a one dimensional periodic lattice, where each site can be in one of the four states say, empty, or occupied by a single predator,…

We present a formalism to derive the stochastic differential equations (SDEs) for several solid-on-solid growth models. Our formalism begins with a mapping of the microscopic dynamics of growth models onto the particle systems with…

The hazard function represents one of the main quantities of interest in the analysis of survival data. We propose a general approach for parametrically modelling the dynamics of the hazard function using systems of autonomous ordinary…

(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…

This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…

We present a computational framework to investigate steady state distributions and perform stability analysis for random ordinary differential equations driven by parameter uncertainty. Using the nonlinear Rosenzweig McArthur predator prey…

In this paper, we develop a kernel learning backward SDE filter method to estimate the state of a stochastic dynamical system based on its partial noisy observations. A system of forward backward stochastic differential equations is used to…

A coarse grained description of a two-dimensional prey-predator system is given in terms of a 3-state lattice model containing two control parameters: the spreading rates of preys and predators. The properties of the model are investigated…

Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets…

In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodies. Such system may be relevant for the modelling of bird…

In many areas, such as the physical sciences, life sciences, and finance, control approaches are used to achieve a desired goal in complex dynamical systems governed by differential equations. In this work we formulate the problem of…

We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally…

We investigate some probabilistic aspects of the unique global strong solution of a two dimensional system of stochastic differential equations describing a prey-predator model perturbed by Gaussian noise. We first establish, for any fixed…

Deterministic flow models, such as rectified flows, offer a general framework for learning a deterministic transport map between two distributions, realized as the vector field for an ordinary differential equation (ODE). However, they are…

This paper is concerned with a mathematical model of competition for resource where species consume noninteracting resources. This system of differential equations is formally obtained by renormalizing the MacArthur's competition model at…

We construct two ordinary-differential-equation models of a predator feeding adaptively on two prey types, and we evaluate the models' ability to fit data on freshwater plankton. We model the predator's switch from one prey to the other in…

We propose a novel predator-prey model that integrate two ecologically significant mechanisms: the Allee effect in the prey population and cooperative hunting behavior among predators. Building upon the Rosenzweig-MacArthur framework, our…

There is an increasing interest in analyzing the behavior of machine learning systems against adversarial attacks. However, most of the research in adversarial machine learning has focused on studying weaknesses against evasion or poisoning…

Many scientific problems focus on observed patterns of change or on how to design a system to achieve particular dynamics. Those problems often require fitting differential equation models to target trajectories. Fitting such models can be…