Dynamic Replicator Equation as a Gradient System
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| Year of publication | 2009 |
| Type | Conference abstract |
| MU Faculty or unit | |
| Citation | |
| Description | 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. |
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