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Related papers: Rate-induced tipping in a solvable model with the …

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In nonlinear dynamical systems, tipping refers to a critical transition from one steady state to another, typically catastrophic, steady state, often resulting from a saddle-node bifurcation. Recently, the machine-learning framework of…

Chaotic Dynamics · Physics 2026-04-09 Smita Deb , Zheng-Meng Zhai , Mulugeta Haile , Ying-Cheng Lai

Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to 'tipping': a 'catastrophic process' in which a system, driven by gradually changing external factors, abruptly transitions (or 'collapses')…

Dynamical Systems · Mathematics 2025-06-30 Dock Staal , Arjen Doelman

Plankton blooms are complex nonlinear phenomena whose occurrence can be described by the two-timescale (fast-slow) phytoplankton-zooplankton model intrpduced by Truscott and Brindley 1994. In their work, they observed that a sufficiently…

Pattern Formation and Solitons · Physics 2022-12-05 Anna Vanselow , Lukas Halekotte , Pinaki Pal , Sebastian Wieczorek , Ulrike Feudel

We study a predator-prey model with Holling type I functional response, an alternative food source for the predator, and multiple Allee effects on the prey. We show that the model has at most two equilibrium points in the first quadrant,…

Dynamical Systems · Mathematics 2020-02-21 Claudio Arancibia-Ibarra , Michael Bode , José Flores , Graeme Pettet , Peter van Heijster

In this article, we have considered a planar slow-fast modified Leslie-Gower predator-prey model with a weak Allee effect in the predator, based on the natural assumption that the prey reproduces far more quickly than the predator. We…

Populations and Evolution · Quantitative Biology 2023-06-26 Tapan Saha , Pallav Jyoti Pal

This paper investigates the dynamical behaviors of a Holling type I Leslie-Gower predator-prey model where the predator exhibits an Allee effect and is subjected to constant harvesting. The model demonstrates three types of equilibrium…

Dynamical Systems · Mathematics 2025-04-02 Jianhang Xie , Changrong Zhu

A predator-prey model with functional response Holling type II, Allee effect in the prey and a generalist predator is considered. It is shown that the model with strong Allee effect has at most two positive equilibrium point in the first…

Dynamical Systems · Mathematics 2020-09-10 Claudio Arancibia-Ibarra , Jos/'e Flores

We consider a recently introduced model of mosquito dynamics that includes mating and progression through breeding, questing and egg-laying stages of mosquitoes using human and other vertebrate sources for blood meals. By exploiting a…

Populations and Evolution · Quantitative Biology 2024-11-12 J. Banasiak , Bime M. Ghakanyuy , Gideon A. Ngwa

In stochastic population dynamics, stochastic wandering can produce transition to an absorbing state. In particular, under Allee effects, low densities amplify the possibility of population collapse. We investigate this in an…

Populations and Evolution · Quantitative Biology 2026-01-13 Luis F. Gordillo , Priscilla E. Greenwood

A demographic Allee effect occurs when individual fitness, at low densities, increases with population density. Coupled with environmental fluctuations in demographic rates, Allee effects can have subtle effects on population persistence…

Probability · Mathematics 2014-05-08 Gregory Roth , Sebastian Schreiber

The equations for quintessential $\alpha$-attractor inflation with a single scalar field, radiation and matter in a spatially flat FLRW spacetime are recast into a regular dynamical system on a compact state space. This enables a complete…

General Relativity and Quantum Cosmology · Physics 2024-02-08 Artur Alho , Claes Uggla

This study introduces an innovative framework for merging ecological and epidemiological modeling via the formulation of a sophisticated predator-prey model that addresses the intricacies of disease dynamics, the Allee effect, and defensive…

Dynamical Systems · Mathematics 2025-05-06 Kwadwo Antwi-Fordjour , Zachary Overton , Dylan Lee

The possibility of rate-induced tipping (R-tipping) away from an attracting fixed point has been thoroughly explored in 1-dimensional systems. In these systems, it is impossible to have R-tipping away from a path of quasi-stable equilibria…

Dynamical Systems · Mathematics 2018-10-08 Claire Kiers , Christopher K. R. T. Jones

We study an acceleration phenomenon arising in monostable integro-differential equations with a weak Allee effect. Previous works have shown its occurrence and have given correct upper bounds on the rate of expansion in some particular…

Analysis of PDEs · Mathematics 2025-10-13 Emeric Bouin , Jérôme Coville , Guillaume Legendre

We study simple stochastic scenarios, based on birth-and-death Markovian processes, that describe populations with Allee effect, to account for the role of demographic stochasticity. In the mean-field deterministic limit we recover…

Statistical Mechanics · Physics 2019-02-06 Vicenç Méndez , Michael Assaf , Axel Masó-Puigdellosas , Daniel Campos , Werner Horsthemke

The theory of alternative stable states and tipping points has garnered substantial attention in the last several decades. It predicts potential critical transitions from one ecosystem state to a completely different state under increasing…

Pattern Formation and Solitons · Physics 2024-09-11 Swarnendu Banerjee , Mara Baudena , Paul Carter , Robbin Bastiaansen , Arjen Doelman , Max Rietkerk

This article is concerned with a stochastic multi-patch model in which each local population is subject to a strong Allee effect. The model is obtained by using the framework of interacting particle systems to extend a stochastic two-patch…

Probability · Mathematics 2013-01-03 Nicolas Lanchier

We investigate the most probable phase portrait (MPPP) of a stochastic single-species model with the Allee effect using the non-local Fokker-Planck equation. This stochastic model is driven by non-Gaussian as well as Gaussian noise, and it…

Dynamical Systems · Mathematics 2023-02-03 Almaz Tesfay , Shenglan Yuan , Daniel Tesfay , James Brannan

A variation in the environment of a system, such as the temperature, the concentration of a chemical solution or the appearance of a magnetic field, may lead to a drift in one of the parameters. If the parameter crosses a bifurcation point,…

Adaptation and Self-Organizing Systems · Physics 2023-08-16 Julia Cantisán , Serhiy Yanchuk , Jesús M. Seoane , Miguel A. F. Sanjuán , Jürgen Kurths

We study the extinction risk of a fragmented population residing on a network of patches coupled by migration, where the local patch dynamics include the Allee effect. We show that mixing between patches dramatically influences the…

Populations and Evolution · Quantitative Biology 2020-02-05 Ohad Vilk , Michael Assaf