Hamiltonian Dynamics of Darwin Systems

Details Hamiltonian Dynamics of Darwin Systems Hamiltonian Dynamics of Darwin Systems

1997-01-11

arxiv.org/abs/physics/9701012v1

Physics

Biological Physics

22 RevTex pages

Scientific paper

10.1016/S0167-2789(97)00179-6

We present a Hamiltonian approach for the wellknown Eigen model of the Darwin selection dynamics. Hamiltonization is carried out by means of the embedding of the population variable space, describing behavior of the system, into the space of doubled dimension by introducing additional dynamic variables. Besides the study of the formalism, we try to interpret its basic elements (phase space, Hamiltonian, geometry of solutions) in terms of the theoretical biology. A geometric treatment is given for the considered system dynamics in terms of the geodesic flows in the Euclidean space where the population variables serve as curvilinear coordinates. The evolution of the distribution function is found for arbitrary distributed initial values of the population variables.

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