相关论文: Population Dynamics with Infinite Leslie Matrices

In this work we study a kinetic model of active particles with delayed dynamics, and its limit when the number of particles goes to infinity. This limit turns out to be related to delayed differential equations with random initial…

Discrete and Continuous Dynamics is the first in a series of articles on Network Models for Epidemiology. This project began in the Fall quarter of 2014 in my continuous modeling course. Since then, it has taken off and turned into a series…

This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…

The aim of this paper is to tackle part of the program set by Diekmann et al. in their seminal paper Diekmann et al. (2001). We quote "It remains to investigate whether, and in what sense, the nonlinear determin-istic model formulation is…

The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…

Many biological systems are governed by difference equations and exhibit discrete-time dynamics. Examples include the size of a population when generations are non-overlapping, and the incidence of a disease when infections are recorded at…

In these notes we present a pedagogical account of the population dynamics methods recently introduced to simulate large deviation functions of dynamical observables in and out of equilibrium. After a brief introduction on large deviation…

Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Inhomogeneous models of populations and communities allow for birth and death rates to vary among…

We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with…

Scaling has been proposed as a powerful tool to analyze the properties of complex systems, and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of…

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…

Modern generative machine learning models demonstrate surprising ability to create realistic outputs far beyond their training data, such as photorealistic artwork, accurate protein structures, or conversational text. These successes…

Input-affine dynamical systems often arise in control and modeling scenarios, such as the data-driven case when state-derivative observations are recorded under bounded noise. Common tasks in system analysis and control include optimal…

The superior Fisher-Kopeliovich closure is applied to the hierarchy of master equations for spatial moments of population dynamics for the first time. As a consequence, the population density, pair and triplet distribution functions are…

We investigate a new model for populations evolving in a spatial continuum. This model can be thought of as a spatial version of the Lambda-Fleming-Viot process. It explicitly incorporates both small scale reproduction events and large…

This paper studies the adaptive optimal control problem for a class of linear time-delay systems described by delay differential equations (DDEs). A crucial strategy is to take advantage of recent developments in reinforcement learning and…

In this paper, we are concerned with the null controllability of a linear population dynamics cascade systems (or the so-called prey-predator models) with two different dispersion coefficients which degenerate in the boundary and with one…

In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties,…

The goal of this paper is to develop data-driven control design and evaluation strategies based on linear matrix inequalities (LMIs) and dynamic programming. We consider deterministic discrete-time LTI systems, where the system model is…

The question of whether biological populations survive or are eventually driven to extinction has long been examined using mathematical models. In this work we study population survival or extinction using a stochastic, discrete…