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@proceedings{852105,
author = {Pospíšil, Zdeněk},
booktitle = {15th ICDEA, International Conference on Difference Equations and Applications. Abstract book, program.},
keywords = {Replicator equation; time scale; bimatrix game; evolutionary dynamics},
language = {eng},
title = {Dynamic Replicator Equation as a Gradient System},
url = {http://isdeds.org/icdea2009/},
year = {2009}
}
TY - CONF
ID - 852105
AU - Pospíšil, Zdeněk
PY - 2009
TI - Dynamic Replicator Equation as a Gradient System
KW - Replicator equation
KW - time scale
KW - bimatrix game
KW - evolutionary dynamics
UR - http://isdeds.org/icdea2009/
N2 - The bimatrix replicator equation describes an evolutionary dynamics for asymmetric conflicts. The phase variables are defined on the interiors of the probability simplexes. In the continuous case and under some assumptions, the equation corresponds to certain gradient system. The contribution introduces a "delta outer derivative" of a function with respect to a function defined on a time scale. The main result presents necessary and sufficient conditions for existence of a function defined on the tangent space to the cartesian product of the simplexes such that its "outer delta derivative" equals to an inner product of RHS,s of the equation with a vector in the tangent space.
ER -
POSPÍŠIL, Zdeněk. Dynamic Replicator Equation as a Gradient System. In \textit{15th ICDEA, International Conference on Difference Equations and Applications. Abstract book, program.}. 2009.
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