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Related papers: Logistic and $\theta$-logistic models in populatio…

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The logistic equation is ubiquitous in applied mathematics as a minimal model of saturating growth. Here, we examine a broad generalisation of the logistic growth model to discretely structured populations, motivated by examples that range…

Populations and Evolution · Quantitative Biology 2025-05-15 Benjamin J. Walker , Helen M. Byrne

In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model dynamical systems subjected to bounded noisy perturbations. In order to discuss the main characteristics of this new approach we consider some basic models in…

Dynamical Systems · Mathematics 2024-01-17 Tomás Caraballo , Renato Colucci , Javier López-de-la-Cruz , Alain Rapaport

We consider a generalization of the classical logistic growth model introducing more than one inflection point. The growth, called multi-sigmoidal, is firstly analyzed from a deterministic point of view in order to obtain the main…

Populations and Evolution · Quantitative Biology 2024-01-31 Antonio Di Crescenzo , Paola Paraggio , Patricia Román-Román , Francisco Torres-Ruiz

We consider excursions for a class of stochastic processes describing a population of discrete individuals experiencing density-limited growth, such that the population has a finite carrying capacity and behaves qualitatively like the…

Populations and Evolution · Quantitative Biology 2017-04-10 Todd L. Parsons

Stochastic models play an essential role in accounting for the variability and unpredictability seen in real-world. This paper focuses on the application of the gamma distribution to analysis of the stationary distributions of populations…

Populations and Evolution · Quantitative Biology 2024-11-18 Haiyan Wang

In this Note, we describe the stationary equilibria and the asymptotic behaviour of an heterogeneous logistic reaction-diffusion equation under the influence of autonomous or time-periodic forcing terms. We show that the study of the…

Analysis of PDEs · Mathematics 2010-06-15 Mickaël D. Chekroun , Lionel Roques

We study an ecology-inspired model for a population of bounded size, whose dynamics is governed by random birth, death, and immigration events. Stochastic fluctuations in the number of individuals give rise to a succession of alternating…

Populations and Evolution · Quantitative Biology 2026-05-27 Lucas M. Brugevin , Damián H. Zanette

We are concerned with a nonlinear nonautonomous model represented by an equation describing the dynamics of an age-structured population diffusing in a space habitat $O,$ governed by local Lipschitz vital factors and by a stochastic…

Analysis of PDEs · Mathematics 2020-04-22 Gabriela Marinoschi

Extinction is the ultimate absorbing state of any stochastic birth-death process, hence the time to extinction is an important characteristic of any natural population. Here we consider logistic and logistic-like systems under the combined…

Populations and Evolution · Quantitative Biology 2019-03-27 Yitzhak Yahalom , Nadav M. Shnerb

This work is devoted to the study of a stochastic logistic growth model with and without the Allee effect. Such a model describes the evolution of a population under environmental stochastic fluctuations and is in the form of a stochastic…

Populations and Evolution · Quantitative Biology 2020-08-05 Almaz Tesfay , Daniel Tesfay , James Brannan , Jinqiao Duan

Logarithmic growth-rates are fundamental observables for describing ecological systems and the characterization of their distributions with analytical techniques can greatly improve their comprehension. Here a neutral model based on a…

Populations and Evolution · Quantitative Biology 2025-01-24 E. Brigatti , S. Azaele

In this paper, we study the initial-boundary value problem and its asymptotic behavior for a repulsive chemotaxis model with logarithmic sensitivity and logistic growth. We establish global well-posedness of strong solutions for large…

Analysis of PDEs · Mathematics 2020-12-22 Padi Fuster Aguilera , Vincent R. Martinez , Kyle Kun Zhao

Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit…

Populations and Evolution · Quantitative Biology 2014-06-02 Coralie Fritsch , Jérôme Harmand , Fabien Campillo

Many unicellular organisms allocate their key proteins asymmetrically between the mother and daughter cells, especially in a stressed environment. A recent theoretical model is able to predict when the asymmetry in segregation of key…

Populations and Evolution · Quantitative Biology 2021-08-11 Jiseon Min , Ariel Amir

We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…

Populations and Evolution · Quantitative Biology 2008-07-31 Alexei J. Drummond , Peter D. Drummond

Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamics models into a simple formula. A physical interpretation is given to…

Biological Physics · Physics 2009-10-20 Alexandre Souto Martinez , Rodrigo Silva Gonzalez , Aquino Lauri Espindola

A central problem in population ecology is understanding the consequences of stochastic fluctuations. Analytically tractable models with Gaussian driving noise have led to important, general insights, but they fail to capture rare,…

Populations and Evolution · Quantitative Biology 2017-12-08 Brandon H. Schlomann

This paper is mainly devoted to lay an empirical foundation for further research on complex spatial dynamics of two-population interaction. Based on the US population census data, a rural and urban population interaction model is developed.…

Physics and Society · Physics 2016-06-14 Yanguang Chen , Feng Xu

Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed…

Statistical Mechanics · Physics 2020-11-11 Bertrand Ottino-Löffler , Mehran Kardar

Lattice-based random walk models are widely used to study populations of migrating cells with motility bias and proliferation. Crowding is typically represented by volume exclusion, where each lattice site can be occupied by at most one…

Populations and Evolution · Quantitative Biology 2026-01-28 Michael J. Plank , Matthew J. Simpson