Journal of Dynamical and Control Systems

, Volume 22, Issue 1, pp 1–14 | Cite as

On Diffusive Stability of Eigen’s Quasispecies Model

  • Alexander S. Bratus
  • Chin-Kun Hu
  • Mikhail V. Safro
  • Artem S. Novozhilov


Eigen’s quasispecies system with explicit space and global regulation is considered. Limit behavior and stability of the system in a functional space under perturbations of the diffusion matrix with non-negative spectrum are investigated. It is proven that if the diffusion matrix has only positive eigenvalues, then the solutions of the distributed system converge to the equilibrium solution of the corresponding local dynamical system. These results imply that many of the properties of the quasispecies model, including the critical mutation rates that specify the infamous error threshold, do not change if the spatial interactions under the principle of global regulation are taken into account.


Eigen’s quasispecies model Reaction–diffusion systems Diffusive instability 

Mathematics Subject Classifications (2010)

Primary: 35K57, 35B35, 91A22 Secondary: 92D25 



This research is supported in part by the Russian Foundation for Basic Research (RFBR) grant #10-01-00374 and joint grant between RFBR and Taiwan National Council #12-01-92004HHC-a. ASN’s research is supported in part by ND EPSCoR and NSF grant #EPS-0814442. CKH is supported in part by Taiwan-Russia collaborative research grant #101-2923-M-001-003-MY3 and NCTS (North).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Alexander S. Bratus
    • 1
  • Chin-Kun Hu
    • 2
  • Mikhail V. Safro
    • 3
  • Artem S. Novozhilov
    • 4
  1. 1.Faculty of Computational Mathematics and CyberneticsLomonosov Moscow State UniversityMoscowRussia
  2. 2.Applied Mathematics–1Moscow State University of Railway EngineeringMoscowRussia
  3. 3.Institute of PhysicsAcademia SinicaTaipeiTaiwan
  4. 4.Department of MathematicsNorth Dakota State UniversityFargoUSA

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