| | |
| | |
Stat |
Members: 3643 Articles: 2'487'895 Articles rated: 2609
28 March 2024 |
|
| | | |
|
Article overview
| |
|
Novel methods to analyze the replicator equation and asymptotical behavior of its solutions | Georgy P Karev
; Artem S Novozhilov
; Faina S Berezovskaya
; | Date: |
26 Jun 2009 | Abstract: | Selection systems and the corresponding replicator equations model the
evolution of replicators with a high level of abstraction. In this paper we
apply novel methods of analysis of selection systems to the replicator
equations. To be suitable for the suggested algorithm the interaction matrix of
the replicator equation should be transformed; in particular the standard
singular value decomposition allows us to rewrite the replicator equation in a
convenient form. The original $n$-dimensional problem is reduced to the
analysis of asymptotic behavior of the solutions to the so-called escort
system, which in some important cases can be of significantly smaller dimension
than the original system. The Newton diagram methods are applied to study the
asymptotic behavior of the solutions to the escort system, when interaction
matrix has rank 1 or 2. A general replicator equation with the interaction
matrix of rank 1 is fully analyzed; the conditions are provided when the
asymptotic state is a polymorphic equilibrium. As an example of the system with
the interaction matrix of rank 2 we consider the problem from [Adams, M.R. and
Sornborger, A.T., J Math Biol, 54:357-384, 2007], for which we show, for
arbitrary dimension of the system and under some suitable conditions, that
generically one globally stable equilibrium exits on the 1-skeleton of the
simplex. | Source: | arXiv, 0906.4986 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |