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We study analytically and numerically a model metabolic cycle composed of an arbitrary number of species of catalytically active particles. Each species converts a substrate into a product, the latter being used as the substrate by the next…

Soft Condensed Matter · Physics 2023-09-29 Vincent Ouazan-Reboul , Jaime Agudo-Canalejo , Ramin Golestanian

Complex change is often described as "evolutionary" in economics, policy, and technology, yet most system dynamics models remain constrained to fixed state spaces and equilibrium-seeking behavior. This paper argues that evolutionary…

Populations and Evolution · Quantitative Biology 2026-02-19 Dan Adler

We study flocking in one dimension, introducing a lattice model in which particles can move either left or right. We find that the model exhibits a continuous nonequilibrium phase transition from a condensed phase, in which a single `flock'…

Statistical Mechanics · Physics 2009-10-31 O. J. O'Loan , M. R. Evans

Recurrence plots and their associated quantifiers provide a robust framework for detecting and characterising complex patterns in non-linear time-series. In this paper, we employ recurrence quantification analysis to investigate the…

Populations and Evolution · Quantitative Biology 2025-07-29 M. S. Palmero , M. Bongestab , N. Marwan

We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in…

Probability · Mathematics 2011-01-21 Sylvie Méléard , Sylvie Roelly

This work deals with the effects of an apex predator on the cyclic competition among three distinct species that follow the rules of the rock-paper-scissors game. The investigation develops standard stochastic simulations but is motivated…

Biological Physics · Physics 2017-06-22 C. A Souza-Filho , D. Bazeia , J. G. G. S. Ramos

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…

Chemical Physics · Physics 2012-12-20 Maria Bruna , S. Jonathan Chapman

If one isolated species (corporation) is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species (corporations) can be expressed by a coupled system of two discrete logistic…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 Ricardo Lopez-Ruiz , Daniele Fournier-Prunaret

Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales,…

Populations and Evolution · Quantitative Biology 2019-06-06 Jonathan R. Potts , Mark A. Lewis

We study the two-species symbiotic contact process (2SCP), recently proposed in [de Oliveira, Santos and Dickman, Phys. Rev. E {\bf 86}, 011121 (2012)] . In this model, each site of a lattice may be vacant or host single individuals of…

Populations and Evolution · Quantitative Biology 2015-06-22 Marcelo M. de Oliveira , Ronald Dickman

We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical…

Statistical Finance · Quantitative Finance 2015-03-10 Philip Rinn , Yuriy Stepanov , Joachim Peinke , Thomas Guhr , Rudi Schäfer

It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic…

Populations and Evolution · Quantitative Biology 2011-09-20 Uwe C. Tauber

We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…

Probability · Mathematics 2022-05-10 Julien Barré , Bastien Fernandez , Grégoire Panel

We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…

Analysis of PDEs · Mathematics 2025-10-09 Vincent Bansaye , Alexandre Bertolino , Ayman Moussa

This paper presents new analytical results for a class of nonlinear parabolic systems of partial different equations with small cross-diffusion which describe the macroscopic dynamics of a variety of large systems of interacting particles.…

Analysis of PDEs · Mathematics 2020-03-04 Luca Alasio , Helene Ranetbauer , Markus Schmidtchen , Marie-Therese Wolfram

Cell cultures exhibit rich and complex behaviors driven by dynamic metabolic interactions among cells. In this work, we present a model that captures these interactions through a framework inspired by statistical mechanics. Using Monte…

Biological Physics · Physics 2025-09-25 A. R. Batista-Tomás , C. Díaz-Faloh , R. Mulet

Rock-paper-scissors games metaphorically model cyclic dominance in ecology and microbiology. In a static environment, these models are characterized by fixation probabilities obeying two different "laws" in large and small well-mixed…

Populations and Evolution · Quantitative Biology 2020-02-26 Robert West , Mauro Mobilia

There is mounting evidence that species interactions often involve long-term memory, with highly-varying waiting times between successive events and long-range temporal correlations. Accounting for memory undermines the common Markovian…

Populations and Evolution · Quantitative Biology 2025-11-24 Ohad Vilk , Mauro Mobilia , Michael Assaf

We consider an aggregation model for two interacting species. The coupling between the species is via their velocities, that incorporate self- and cross-interactions. Our main interest is categorizing the possible steady states of the…

Analysis of PDEs · Mathematics 2016-12-26 Joep H. M. Evers , Razvan C. Fetecau , Theodore Kolokolnikov

Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…

Statistical Mechanics · Physics 2007-05-23 Arne Traulsen , Jens Christian Claussen , Christoph Hauert