Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Phase transition in random catalytic networks.

Rudolf Hanel1, Stuart A Kauffman, Stefan Thurner

  • 1Institute of Physics, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Reply to Górski et al.: Polarization requires opinions, not just negative ties.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Adaptive self-organization of global swidden forests.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Supply chain network rewiring dynamics at the firm level.

PNAS nexus·2026
Same author

Inferring firm-level supply chain networks with realistic systemic risk from industry sector-level data.

Scientific reports·2026
Same author

Empirical Validation of the Polarization Transition in a Double-Random Field Model of Elections.

Physical review letters·2026
Same author

Systemic risk mitigation in supply chains through network rewiring.

Scientific reports·2026
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

Autocatalytic networks drive diversity in evolution and systems. This study analytically models these networks, revealing a phase transition in product diversity based on initial conditions and rule density.

Area of Science:

  • Complexity Science
  • Theoretical Biology
  • Systems Chemistry

Background:

  • Autocatalytic networks are fundamental to understanding rapid diversity increases in biological, social, and economic systems.
  • The precise mechanisms governing diversity outcomes in catalytic random networks remain an area of active research.

Purpose of the Study:

  • To analytically investigate the final product diversity in catalytic random networks.
  • To identify the key parameters influencing diversity and explore the existence of phase transitions.

Main Methods:

  • Mapping the catalytic network problem onto a set of nonlinear recurrence equations.
  • Solving these equations to analyze the dependence of product diversity on initial conditions and rule density.

Related Experiment Videos

Main Results:

  • The final number of products critically depends on the initial number of products and the density of catalytic production rules.
  • A phase transition is demonstrated, shifting from a low-diversity to a high-diversity regime for a fixed rule density.
  • The origin of this transition is explained as a crossover between solutions of a quadratic equation.

Conclusions:

  • Analytical solutions for catalytic random networks reveal a critical phase transition in product diversity.
  • The findings offer insights comparable to phase transitions observed in standard thermodynamics (e.g., PVT diagrams).
  • This work provides a framework for understanding diversity generation in complex systems.