Tag Archives: Replicator equation

Another paper

Our already long list of papers devoted to the analysis of a replicator equation became longer with a new paper by Alexander Bratus, Volodya Posvyanskii and myself, “Solutions with a bounded support promote permanence of a distributed replicator equation,” which … Continue reading

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Modeling biological evolution

Here is the latest issue of Mathematical Modelling of Natural Phenomena devoted to the modeling of biological evolution: link This volume includes my (with co-authors) paper Replicator Equations and Space, which is somewhat different from the arXiv version in a few … Continue reading

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Replicator equations and space

Here is a recent paper by Alexander Bratus, Vladimir Posvyanskii, and yself, that we uploaded to arXiv: Replicator equations and space We chose quite an ad hoc method to model the spatial evolution of the frequencies of interacting species, but the … Continue reading

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Cooperative RNA replicators and the origin of life

A recent Nature paper concerning cooperative networks of RNA molecules. Here is the abstract: The origins of life on Earth required the establishment of self-replicating chemical systems capable of maintaining and evolving biological information. In an RNA world, single self-replicating … Continue reading

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Lectures on Mathematical foundations of evolutionary theory

I looked through my lectures on the course I gave twice during the last couple of years and made some small changes, fixed a few typos, etc. Here are all the lectures together, in Russian: Lecture 0: A naive introduction … Continue reading

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Prisoner’s Dilemma in Action


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Joint Mathematics Meeting 2012, Boston

January 4-7 I attended Joint Mathematics Meeting held this year in Boston, Massachusetts. Although  in the program of this meeting my name in only for one presentation, I managed to give another one at one of the special session on Recent Advances in Mathematical … Continue reading

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A crash course in evolutionary game theory

I prepared these notes (in Russian) to test my students. This is a very short account of evolutionary game theory and applications of the replicator equation. There are wonderful books in English (see the references in the text) of any … Continue reading

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Seminar at Steklov Institue, Department of Mathematical Physics

Today, November 3, I gave a presentation to the Department of Mathematical Physics, Steklov Institute in Moscow (I was invited by Sergei Kozyrev). The presentation was on the solutions to the replicator equation. The slides (slightly different) can be found … Continue reading

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Solutions to the replicator equations

I gave a presentation on the asymptotic solutions to the replicator equation where the matrix is given by for three non-negative vectors . The presentation was at Yulij Ilyashenko‘s seminar at Steklov Institute in Moscow. The slides can be found … Continue reading

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