2 citations · 4 across the 6 of their papers we have counts for
6 papers
On the scope of applicability of the models of Darwinian dynamics
Georgiy Karev
In their well-known textbook (Vincent & Brown, 2005), Vincent and Brown suggested an attractive approach for studying evolutionary dynamics of populations that are heterogeneous wi…
Dynamics of Strategy Distribution in a One-Dimensional Continuous Trait Space with a Bi-linear and Quadratic Payoff Functions
Georgiy Karev
Evolution of distribution of strategies in game theory is an interesting question that has been studied only for specific cases. Here I develop a general method to extend analysis…
Arnold weak resonance equation as the model of Greek ornamental design
Faina Berezovskaya, Georgiy Karev
We propose and study a mathematical model that qualitatively reproduces several ancient ornamental designs than one can see in historical museums of Crete and Athens. The designs c…
Replicator equations and the principle of minimal production of information
Georgiy P. Karev
Many complex systems in mathematical biology and other areas can be described by the replicator equation. We show that solutions of a wide class of replicator equations minimize th…
On mathematical theory of selection: Continuous time population dynamics
Georgy P. Karev
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribu…
Bifurcations of self-similar solutions of the Fokker-Plank Equation
F. Berezovskaya, G. Karev
A class of one-dimensional Fokker-Plank equations having a common stationary solution, which is a power function of the state of the process, was found. We prove that these equatio…