On Diffusive Stability of Eigen’s Quasispecies Model

被引:0
|
作者
Alexander S. Bratus
Chin-Kun Hu
Mikhail V. Safro
Artem S. Novozhilov
机构
[1] Lomonosov Moscow State University,Faculty of Computational Mathematics and Cybernetics
[2] Moscow State University of Railway Engineering,Applied Mathematics–1
[3] Academia Sinica,Institute of Physics
[4] North Dakota State University,Department of Mathematics
来源
Journal of Dynamical and Control Systems | 2016年 / 22卷
关键词
Eigen’s quasispecies model; Reaction–diffusion systems; Diffusive instability; Primary: 35K57, 35B35, 91A22; Secondary: 92D25;
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摘要
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.
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页码:1 / 14
页数:13
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