pith. sign in

arxiv: 2606.25682 · v1 · pith:5HKIYXONnew · submitted 2026-06-24 · ⚛️ physics.soc-ph · cs.SI· math.DS

Opinion Dynamics over Migration Networks

L\H{o}rinc M\'arton , Stefanie Winkelmann , Mauricio J. del Razo , Nata\v{s}a Djurdjevac Conrad This is my paper

Pith reviewed 2026-06-25 20:04 UTC · model grok-4.3

classification ⚛️ physics.soc-ph cs.SImath.DS
keywords opinion dynamicsmigration networksstochastic processesmaster equationconsensuspolarizationdemographic change
0
0 comments X

The pith

A stochastic master equation couples opinion changes, births and deaths, and migration to produce consensus, polarization, and stabilized opinion cycles.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper builds a probabilistic model of populations in which individuals hold opinions, move between places, and experience random births and deaths. The model starts from a single master equation that tracks all three processes at once and then derives simpler equations for average community sizes and opinion shares. Case studies show that including chance and movement produces collective behaviors such as sudden agreement, lasting division, or steady swings that steady non-random models do not produce. The work treats migration as an active driver inside opinion formation rather than an outside force. Readers would care because everyday social change involves moving people whose views interact across locations.

Core claim

The central discovery is a unifying stochastic framework for opinion dynamics over migration networks that couples local opinion transitions, demographic processes and migration between communities. The dynamics are formulated through a spatio-temporal master equation, which provides a probabilistic description of the underlying population process. From this microscopic representation, deterministic mean-field equations are derived that govern the co-evolution of community sizes and opinion compositions. Two case studies demonstrate that stochasticity and migration can qualitatively change emergent dynamics and collective outcomes, including the emergence of consensus, polarization and the s

What carries the argument

The spatio-temporal master equation that simultaneously encodes local opinion transitions, demographic birth-death processes, and migration flows between communities.

If this is right

  • Deterministic models without stochasticity or migration miss certain transitions between collective states.
  • Migration flows can stabilize oscillatory opinion dynamics that would otherwise persist or decay.
  • Community sizes and opinion shares co-evolve through the derived mean-field equations.
  • Finite-size fluctuations and random transitions become visible only in the stochastic formulation.
  • Migration must be treated as an internal component of opinion formation rather than an external demographic input.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same master-equation structure could be used to track cultural traits or voting preferences that travel with migrating populations.
  • Surveys that record both residence changes and opinion shifts over time could directly test whether the predicted qualitative changes appear.
  • Adjusting migration rates in the model would offer a way to explore how movement policies might affect levels of political division.

Load-bearing premise

A single master equation can be written that accurately combines opinion transitions, demographic processes, and migration without extra unstated interaction terms that would remove the claimed qualitative changes.

What would settle it

Real data from a migration network in which opinion patterns show no difference in consensus, polarization, or oscillation behavior between versions that include versus exclude stochasticity and migration.

Figures

Figures reproduced from arXiv: 2606.25682 by L\H{o}rinc M\'arton, Mauricio J. Del Razo, Nata\v{s}a Djurdjevac Conrad, Stefanie Winkelmann.

Figure 1
Figure 1. Figure 1: Components of the system dynamics. 1. Local transitions, occurring within each community and consisting of: • Opinion transitions, describing changes in individual opinions due to social inter￾actions or external influences (e.g., media exposure or political factors). • Local demographics, accounting for changes in community size through inflow and outflow of agents (e.g. births and deaths). 2. Migration, … view at source ↗
Figure 2
Figure 2. Figure 2: Bifurcation diagram and phase-space analysis. a. Schematic illustration of the two-community opinion dynamics model with bidirectional migration and two opinions ”Yes” and ”No”. b. Bifurcation diagram showing the emergence of two additional stable equilibria as the ratio γ/µ increases, in agreement with Eqs. (4.11) to (4.13). c. Phase portrait in the (x (1) Y , x (2) Y )-plane for migration-induced consens… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of deterministic and stochastic dynamics in the conformity-induced polarization regime (µ = 1, γ = 40). a. Deterministic solution of Eq. (3.15) for the initial condition x (1) Y = 0.2 x (2) Y = 0.6. b, c. Two realizations of the stochastic process (3.3) starting from the same initial condition. While the trajectory in b converges to the same equilibrium as the deterministic solution, the traject… view at source ↗
Figure 4
Figure 4. Figure 4: Example with three interconnected communities and three possible opinions. a. Schematic illustration of the opinion dynamics over the migration network. b. Opinion dynamics without migration. Four plots are shown: total population number in each com￾munity (top left) and the fraction of agents of the three opinions in community C1 (top right), C2 (bottom left) and C3 (bottom right). c. The same four plots … view at source ↗
read the original abstract

Opinions play a crucial role in shaping collective phenomena such as political polarization, cultural integration and demographic change. By continuously changing social environments in which opinions evolve, human migration serves as an important driver of collective opinion formation. While migration and opinion dynamics have both been extensively studied, the few existing models that couple the two are primarily deterministic and therefore cannot capture demographic fluctuations, finite-size effects or stochastic transitions between emergent collective states. To address this limitation, we introduce a unifying stochastic framework for opinion dynamics over migration networks that couples local opinion transitions, demographic processes and migration between communities. The dynamics are formulated through a spatio--temporal master equation, which provides a probabilistic description of the underlying population process. From this microscopic representation, we derive deterministic mean-field equations governing the co-evolution of community sizes and opinion compositions, thereby linking agent-level interactions to macroscopic population behavior. Using two representative case studies, we demonstrate how stochasticity and migration can qualitatively change the emergent dynamics and collective outcomes, including the emergence of consensus, polarization and the stabilization of oscillatory opinion dynamics. These examples highlight the rich interplay between social interactions, demographic change and migration in deterministic and stochastic settings, and they demonstrate that migration should be viewed as an integral component of collective opinion formation rather than only an external demographic process.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript introduces a unifying stochastic framework for opinion dynamics over migration networks. It formulates the coupled processes of local opinion transitions, demographic birth-death processes, and inter-community migration via a single spatio-temporal master equation, derives deterministic mean-field equations for community sizes and opinion compositions, and uses two case studies to demonstrate that stochasticity and migration can qualitatively alter collective outcomes including consensus, polarization, and stabilization of oscillations.

Significance. If the central construction and derivations hold, the work supplies a principled stochastic-to-deterministic link for social dynamics that treats migration as an endogenous driver rather than an external parameter; the explicit master-equation starting point and the reported qualitative distinctions between stochastic and deterministic regimes are strengths that could inform subsequent modeling in sociophysics.

minor comments (3)
  1. [mean-field derivation section] The abstract states that mean-field equations are derived from the master equation, but the manuscript should explicitly state the closure or approximation steps used in that derivation (e.g., in the section presenting the mean-field limit) to allow readers to assess when the qualitative changes survive the limit.
  2. [case-studies section] The two case studies are described as representative, yet the specific functional forms chosen for the opinion-transition rates and migration probabilities are not compared against alternative functional forms; a brief sensitivity check would strengthen the claim that the reported behaviors are generic rather than model-specific.
  3. [model-formulation section] Notation for the state variables (e.g., community size N_i and opinion fraction x_i) should be introduced once with a clear table or list of symbols to avoid ambiguity when the master equation is written in component form.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript, the accurate summary of its contributions, and the recommendation for minor revision. No major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper formulates a spatio-temporal master equation as the central modeling step to couple opinion transitions, demographic birth-death processes, and migration flows, then derives deterministic mean-field equations from this microscopic representation. This constitutes a standard forward derivation from a probabilistic description to macroscopic equations, with no reduction of any claimed prediction or qualitative outcome (consensus, polarization, oscillatory stabilization) to a fitted parameter or self-referential definition. Case studies illustrate emergent behaviors from the constructed dynamics rather than tautologically reproducing inputs. No self-citation load-bearing steps, ansatz smuggling, or renaming of known results are present in the provided text. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms or invented entities; the master-equation construction itself is treated as a standard modeling choice whose validity is not audited here.

pith-pipeline@v0.9.1-grok · 5776 in / 1204 out tokens · 24108 ms · 2026-06-25T20:04:57.837575+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

64 extracted references · 1 linked inside Pith

  1. [1]

    A data-driven kinetic model for opinion dynamics with social network contacts

    Giacomo Albi, Elisa Calzola, and Giacomo Dimarco. A data-driven kinetic model for opinion dynamics with social network contacts. European Journal of Applied Mathe- matics, 36(2):264–290, 2025. 25

    2025

  2. [2]

    Opinion dynamics over com- plex networks: Kinetic modelling and numerical methods

    Giacomo Albi, Lorenzo Pareschi, and Mattia Zanella. Opinion dynamics over com- plex networks: Kinetic modelling and numerical methods. Kinetic and Related Models , 10(1):1–32, 2017

    2017

  3. [3]

    Anderson and Thomas G

    David F. Anderson and Thomas G. Kurtz. Stochastic analysis of biochemical systems , volume 674. Springer, 2015

    2015

  4. [4]

    Opinion polarization by learning from social feed- back

    Sven Banisch and Eckehard Olbrich. Opinion polarization by learning from social feed- back. The Journal of Mathematical Sociology , 43(2):76–103, 2019

    2019

  5. [5]

    James, Maxime Lenor- mand, Thomas Louail, Ronaldo Menezes, José J

    Hugo Barbosa, Marc Barthelemy, Gourab Ghoshal, Charlotte R. James, Maxime Lenor- mand, Thomas Louail, Ronaldo Menezes, José J. Ramasco, Filippo Simini, and Marcello Tomasini. Human mobility: Models and applications. Physics Reports, 734:1–74, 2018

    2018

  6. [6]

    Intergroup contact and negative attitudes towards immigrants among youth in Sweden: Individual and contextual factors

    Beint Magnus Aamodt Bentsen. Intergroup contact and negative attitudes towards immigrants among youth in Sweden: Individual and contextual factors. Journal of International Migration and Integration , 23(1):243–266, 2022

    2022

  7. [7]

    The scaling laws of human travel

    Dirk Brockmann, Lars Hufnagel, and Theo Geisel. The scaling laws of human travel. Nature, 439(7075):462–465, Jan 2006

    2006

  8. [8]

    Statistical physics of social dynamics

    Claudio Castellano, Santo Fortunato, and Vittorio Loreto. Statistical physics of social dynamics. Reviews of Modern Physics , 81(2):591–646, 2009

    2009

  9. [9]

    International migration as a driver of political and social change: Evidence from Morocco

    Hein de Haas, Frédéric Docquier, and Maurice Schiff. International migration as a driver of political and social change: Evidence from Morocco. Journal of Population Economics, 32:1171–1203, 2019

    2019

  10. [10]

    del Razo and Margarita Kostré

    Mauricio J. del Razo and Margarita Kostré. Open reaction-diffusion systems: bridging probabilistic theory and simulations across scales. Journal of Physics A: Mathematical and Theoretical, 58(14):145001, 2025

    2025

  11. [11]

    del Razo, Tommaso Lamma, and Wout Merbis

    Mauricio J. del Razo, Tommaso Lamma, and Wout Merbis. Field theories and quan- tum methods for stochastic reaction-diffusion systems. Reviews of Modern Physics , 98(1):015001, 2026

    2026

  12. [12]

    del Razo, Hong Qian, and Frank Noé

    Mauricio J. del Razo, Hong Qian, and Frank Noé. Grand canonical diffusion-influenced reactions: A stochastic theory with applications to multiscale reaction-diffusion simu- lations. The Journal of Chemical Physics , 149(4):044102, 2018

    2018

  13. [13]

    Feedback loops in opin- ion dynamics of agent-based models with multiplicative noise

    Nataša Djurdjevac Conrad, Jonas Köppl, and Ana Djurdjevac. Feedback loops in opin- ion dynamics of agent-based models with multiplicative noise. Entropy, 24(10):1352, 2022

    2022

  14. [14]

    Second quantization representation for classical many-particle system

    Masao Doi. Second quantization representation for classical many-particle system. Jour- nal of Physics A: Mathematical and General , 9(9):1465, 1976. 26

    1976

  15. [15]

    Jonathan Chapman

    Radek Erban and S. Jonathan Chapman. Stochastic modelling of reaction–diffusion processes: algorithms for bimolecular reactions. Physical Biology, 6(4):046001, 2009

    2009

  16. [16]

    Jonathan Chapman

    Radek Erban and S. Jonathan Chapman. Stochastic modelling of reaction–diffusion processes, volume 60. Cambridge University Press, 2020

    2020

  17. [17]

    Mapping citizens’ attitudes towards soil ecosystem services: A case study from New South Wales, Australia

    Luisa Eusse-Villa, Alex McBratney, Cristiano Franceschinis, Jürgen Meyerhoff, Damien Field, and Mara Thiene. Mapping citizens’ attitudes towards soil ecosystem services: A case study from New South Wales, Australia. Soil Security, 7:100063, 2022

    2022

  18. [18]

    Electoral Shocks: The Volatile Voter in a Turbulent World

    Edward Fieldhouse, Jane Green, Geoffrey Evans, Jonathan Mellon, Christopher Prosser, Hermann Schmitt, and Cees van der Eijk. Electoral Shocks: The Volatile Voter in a Turbulent World. Oxford University Press, 2019

    2019

  19. [19]

    Traditions of tolerance: The long-run persistence of regional variation in attitudes towards English immigrants

    David Fielding. Traditions of tolerance: The long-run persistence of regional variation in attitudes towards English immigrants. British Journal of Political Science , 48(1):167– –188, 2018

    2018

  20. [20]

    Stochastic methods, volume 4

    Crispin Gardiner. Stochastic methods, volume 4. Springer Berlin Heidelberg, 2009

    2009

  21. [21]

    Gibson and Jehoshua Bruck

    Michael A. Gibson and Jehoshua Bruck. Efficient exact stochastic simulation of chemical systems with many species and many channels. The Journal of Physical Chemistry A , 104(9):1876–1889, 2000

    2000

  22. [22]

    Exact stochastic simulation of coupled chemical reactions

    Daniel T Gillespie. Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry , 81(25):2340–2361, 1977

    1977

  23. [23]

    Contrarian voter model under the influence of an oscillating propaganda: Consensus, bimodal behavior and stochastic resonance

    Maria Cecilia Gimenez, Luis Reinaudi, and Federico Vazquez. Contrarian voter model under the influence of an oscillating propaganda: Consensus, bimodal behavior and stochastic resonance. Entropy, 24(8):1140, 2022

    2022

  24. [24]

    Goerg, Andreas Pondorfer, and Valentina Stöhr

    Sebastian J. Goerg, Andreas Pondorfer, and Valentina Stöhr. Regional variation in social norm nudges. Scientific Reports, 14(1):16773, Jul 2024

    2024

  25. [25]

    Cultural transmission and political attitudes: Explaining differences between natives and immigrants in Western Europe

    Jérôme Gonnot and Federica lo Polito. Cultural transmission and political attitudes: Explaining differences between natives and immigrants in Western Europe. Working Paper 2023-12, CEPII research center, May 2023

    2023

  26. [26]

    Haddad, Vijay Sekhar Chellaboina, and Qing Hui

    Wassim M. Haddad, Vijay Sekhar Chellaboina, and Qing Hui. Nonnegative and Com- partmental Dynamical Systems . Princeton University Press, 2010

    2010

  27. [27]

    Strong convergence rates for Markovian representations of fractional processes

    Philipp Harms. Strong convergence rates for Markovian representations of fractional processes. https://arxiv.org/abs/1902.01471, 2019

    arXiv 1902

  28. [28]

    The replicator equation as an inference dynamic

    Marc Harper. The replicator equation as an inference dynamic. https://arxiv.org/abs/0911.1763, 2009. 27

    Pith/arXiv arXiv 2009

  29. [29]

    Opinion dynamics and bounded confidence: models, analysis and simulation

    Rainer Hegselmann and Ulrich Krause. Opinion dynamics and bounded confidence: models, analysis and simulation. Journal of Artificial Societies and Social Simulation , 5(3), 2002

    2002

  30. [30]

    Modelling opinion dynamics under the impact of influencer and media strate- gies

    Luzie Helfmann, Nataša Djurdjevac Conrad, Philipp Lorenz-Spreen, and Christof Schütte. Modelling opinion dynamics under the impact of influencer and media strate- gies. Scientific Reports, 13(1):19375, 2023

    2023

  31. [31]

    Evolutionary games and population dynamics

    Josef Hofbauer and Karl Sigmund. Evolutionary games and population dynamics . Cam- bridge university press, 1998

    1998

  32. [32]

    Holley and Thomas M

    Richard A. Holley and Thomas M. Liggett. Ergodic theorems for weakly interacting infinite systems and the voter model. The Annals of Probability , 3(4), 1975

    1975

  33. [33]

    A multilevel spatial model to investigate voting behaviour in the 2019 UK general election

    Kevin Horan, Chris Brunsdon, and Katarina Domijan. A multilevel spatial model to investigate voting behaviour in the 2019 UK general election. Applied Spatial Analysis and Policy , 17(2):703–727, Jun 2024

    2019

  34. [34]

    Isaacson

    Samuel A. Isaacson. A convergent reaction-diffusion master equation. The Journal of chemical physics, 139(5), 2013

    2013

  35. [35]

    Isaacson, Jingwei Ma, and Konstantinos Spiliopoulos

    Samuel A. Isaacson, Jingwei Ma, and Konstantinos Spiliopoulos. Mean field limits of particle-based stochastic reaction-diffusion models. SIAM Journal on Mathematical Analysis, 54(1):453–511, 2022

    2022

  36. [36]

    Does Emigration Affect Political and Institutional Development in Mi- grants’ Countries of Origin? , pages 761–783

    Artjoms Ivlevs. Does Emigration Affect Political and Institutional Development in Mi- grants’ Countries of Origin? , pages 761–783. Springer International Publishing, Cham, 2021

    2021

  37. [37]

    del Razo

    Margarita Kostré, Christof Schütte, Frank Noé, and Mauricio J. del Razo. Cou- pling particle-based reaction-diffusion simulations with reservoirs mediated by reaction- diffusion PDEs. Multiscale Modeling & Simulation , 19(4):1659–1683, 2021

    2021

  38. [38]

    Thomas G. Kurtz. Solutions of ordinary differential equations as limits of pure jump Markov processes. Journal of Applied Probability , 7(1):49–58, 1970

    1970

  39. [39]

    Thomas G. Kurtz. The relationship between stochastic and deterministic models for chemical reactions. The Journal of Chemical Physics , 57(7):2976–2978, 1972

    1972

  40. [40]

    Stewart Fotheringham

    Ziqi Li and A. Stewart Fotheringham. The spatial and temporal dynamics of voter preference determinants in four U.S. presidential elections (2008–2020). Transactions in GIS , 26(3):1609–1628, 2022

    2008

  41. [41]

    Aden, Neil F

    Jiazhen Liu, Shengda Huang, Nathaniel M. Aden, Neil F. Johnson, and Chaoming Song. Emergence of polarization in coevolving networks. Physics Review Letters , 130:037401, Jan 2023. 28

    2023

  42. [42]

    Hangos, and Attila Magyar

    Lőrinc Márton, Katalin M. Hangos, and Attila Magyar. Migration-connected networks of Lotka–Volterra and quasi-polynomial systems: modeling and decentralized control. Nonlinear Dynamics , 113(9):10577–10596, May 2025

    2025

  43. [43]

    Diffusion-driven pattern formation in an opinion dynam- ical network model

    Tim Mauch and Thilo Gross. Diffusion-driven pattern formation in an opinion dynam- ical network model. Phys. Rev. E , 113:064302, Jun 2026

    2026

  44. [44]

    Analyzing political preferences of second-generation immigrants across the rural–urban divide

    Simone Moriconi, Giovanni Peri, and Riccardo Turati. Analyzing political preferences of second-generation immigrants across the rural–urban divide. Journal of Urban Eco- nomics, 146:103740, 2025

    2025

  45. [45]

    Modeling and migration-based control of depopulation

    Lőrinc Márton. Modeling and migration-based control of depopulation. Theoretical Population Biology, 148:86–94, 2022

    2022

  46. [46]

    O’Meara, Stephen Karuru, Louis E

    Wendy P. O’Meara, Stephen Karuru, Louis E. Fazen, Julius Koech, Brian Kizito, Car- ren Tarus, and Diana Menya. Heterogeneity in health seeking behaviour for treat- ment, prevention and urgent care in four districts in western Kenya. Public Health , 128(11):993–1008, 2014

    2014

  47. [47]

    The effect of income and immigration policies on international migration

    Francesc Ortega and Giovanni Peri. The effect of income and immigration policies on international migration. Migration Studies, 1(1):47–74, 2013

    2013

  48. [48]

    Path integral approach to birth-death processes on a lattice

    Luca Peliti. Path integral approach to birth-death processes on a lattice. Journal de Physique, 46(9):1469–1483, 1985

    1985

  49. [49]

    Sampson, Juan G

    Corbit R. Sampson, Juan G. Restrepo, and Mason A. Porter. Oscillatory and excitable dynamics in an opinion model with group opinions. Physical Review E , 112:024303, 2025

    2025

  50. [50]

    Frank Schweitzer and Janusz A. Hołyst. Modelling collective opinion formation by means of active brownian particles. The European Physical Journal B - Condensed Matter and Complex Systems , 15(4):723–732, Jun 2000

    2000

  51. [51]

    Migrant and non-migrant views on immigration in Europe

    Michaela Šedovič and Lenka Dražanová. Migrant and non-migrant views on immigration in Europe. European Journal of Population , 41(1):13, 2025

    2025

  52. [52]

    González, Amos Maritan, and Albert-László Barabási

    Filippo Simini, Marta C. González, Amos Maritan, and Albert-László Barabási. A universal model for mobility and migration patterns. Nature, 484(7392):96–100, Apr 2012

    2012

  53. [53]

    From diffusion in compartmentalized media to non-Gaussian random walks

    Jakub Ślkezak and Stanislav Burov. From diffusion in compartmentalized media to non-Gaussian random walks. Scientific Reports, 11(1):5101, 2021

    2021

  54. [54]

    Smith and Christian A

    Cameron A. Smith and Christian A. Yates. Spatially extended hybrid methods: a review. Journal of The Royal Society Interface , 15(139):20170931, 2018. 29

    2018

  55. [55]

    Stokes, Samuel E

    Beth M. Stokes, Samuel E. Jackson, Philip Garnett, and Jingxi Luo. Extremism, seg- regation and oscillatory states emerge through collective opinion dynamics in a novel agent-based model. The Journal of Mathematical Sociology , 48(1):42–80, 2024

    2024

  56. [56]

    Opinion evolution in closed community

    Katarzyna Sznajd-Weron and Józef Sznajd. Opinion evolution in closed community. International Journal of Modern Physics C , 11(06):1157–1165, 2000

    2000

  57. [57]

    Stochastic processes in physics and chemistry, volume 1

    Nicolaas Godfried Van Kampen. Stochastic processes in physics and chemistry, volume 1. Elsevier, 1992

    1992

  58. [58]

    Vitanov, Marcel Ausloos, and Giula Rotundo

    Nikolay K. Vitanov, Marcel Ausloos, and Giula Rotundo. Discrete model of ideological struggle accounting for migration. Advances in Complex Systems , 15(supp01):1250049, 2012

    2012

  59. [59]

    Opinion evolution in divided community

    Tomasz Weron and Janusz Szwabiński. Opinion evolution in divided community. En- tropy, 24(2), 2022

    2022

  60. [60]

    The spatiotemporal master equation: Ap- proximation of reaction-diffusion dynamics via Markov state modeling

    Stefanie Winkelmann and Christof Schütte. The spatiotemporal master equation: Ap- proximation of reaction-diffusion dynamics via Markov state modeling. The Journal of Chemical Physics , 145(21), 2016

    2016

  61. [61]

    Hybrid models for chemical reaction net- works: Multiscale theory and application to gene regulatory systems

    Stefanie Winkelmann and Christof Schütte. Hybrid models for chemical reaction net- works: Multiscale theory and application to gene regulatory systems. The Journal of Chemical Physics , 147(11):114115, 2017

    2017

  62. [62]

    Stochastic Dynamics in Computational Biology

    Stefanie Winkelmann and Christof Schütte. Stochastic Dynamics in Computational Biology. Springer, 2020

    2020

  63. [63]

    Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading

    Stefanie Winkelmann, Johannes Zonker, Christof Schütte, and Nataša Djurdjevac Con- rad. Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading. Mathematical Biosciences, 336:108619 – 108619, 2021

    2021

  64. [64]

    Mean-field optimal control with stochastic leaders

    Sebastian Zimper, Ana Djurdjevac, Carsten Hartmann, Christof Schütte, and Nataša Djurdjevac Conrad. Mean-field optimal control with stochastic leaders. https://arxiv.org/abs/2512.19201, 2025. 30

    arXiv 2025