3 citations · 5 across the 5 of their papers we have counts for
6 papers
Solutions with a bounded support promote permanence of a distributed replicator equation
Alexander S. Bratus, Vladimir P. Posvyanskii, Artem S. Novozhilov
The now classical replicator equation describes a wide variety of biological phenomena, including those in theoretical genetics, evolutionary game theory, or in the theories of the…
Asymptotic behavior of spatially distributed replicator systems
Alexander S. Bratus, Artem S. Novozhilov, Vladimir P. Posvyanskii
The question of biological stability (permanence) of a replicator reaction-diffusion system is considered. Sufficient conditions of biological stability are found. It is proved tha…
Replicator equations and space
Artem S. Novozhilov, Vladimir P. Posvyanskii, Alexander S. Bratus
A reaction--diffusion replicator equation is studied. A novel method to apply the principle of global regulation is used to write down the model with explicit spatial structure. Pr…
On the reaction-diffusion replicator systems: Spatial patterns and asymptotic behavior
Artem S. Novozhilov, Vladimir P. Posvyanskii, Alexander S. Bratus
The replicator equation is ubiquitous for many areas of mathematical biology. One of major shortcomings of this equation is that it does not allow for an explicit spatial structure…
A note on the replicator equation with explicit space and global regulation
Alexander S. Bratus', Vladimir P. Posvyanskii, Artem S. Novozhilov
A replicator equation with explicit space and global regulation is considered. This model provides a natural framework to follow frequencies of species that are distributed in the…
Existence and stability of stationary solutions to spatially extended autocatalytic and hypercyclic systems under global regulation and with nonlinear growth rates
Alexander S. Bratus', Vladimir P. Posvyanskii, Artem S. Novozhilov
Analytical analysis of spatially extended autocatalytic and hypercyclic systems is presented. It is shown that spatially explicit systems in the form of reaction-diffusion equation…