Related papers: Discrete vs. continuous dynamics in biology: When …
We compare two approaches to the predictive modeling of dynamical systems from partial observations at discrete times. The first is continuous in time, where one uses data to infer a model in the form of stochastic differential equations,…
This article shows how to specify and construct a discrete, stochastic, continuous-time model specifically for ecological systems. The model is more broad than typical chemical kinetics models in two ways. First, using time-dependent hazard…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
We prove that the standard discrete-time accelerator equation cannot be considered as an exact discrete analog of the continuous-time accelerator equation. This leads to fact that the standard discrete-time macroeconomic models cannot be…
In this paper we analyze a continuous-time epidemic model and its discrete counterpart, where infection spreads both horizontally and vertically. We consider three cases: model with horizontal and imperfect vertical transmissions, model…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
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…
This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…
We propose a model in which dividend payments occur at regular, deterministic intervals in an otherwise continuous model. This contrasts traditional models where either the payment of continuous dividends is controlled or the dynamics are…
Understanding the stability of complex communities is a central focus in ecology, many important theoretical advancements have been made to identify drivers of ecological stability. However, previous results often rely on the…
We propose a nonstandard finite difference scheme for the Susceptible-Infected-Removed (SIR) continuous model. We prove that our discretized system is dynamically consistent with its continuous counterpart and we derive its exact solution.…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
Causal ordering of key events in the cell cycle is essential for proper functioning of an organism. Yet, it remains a mystery how a specific temporal program of events is maintained despite ineluctable stochasticity in the biochemical…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…