Hamiltonian dynamics of Darwin systems

A. V. Shapovalov, E. V. Evdokimov

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We present a Hamiltonian approach for the well-known 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 auxiliary dynamic variables. Besides the study of the formalism, we try to interpret its basic elements (phase space, Hamiltonian, geometry of solutions) in terms of 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. Time evolution of the distribution function is found for arbitrary distributed initial values of the population variables.

Original languageEnglish
Pages (from-to)441-450
Number of pages10
JournalPhysica D: Nonlinear Phenomena
Volume112
Issue number3-4
Publication statusPublished - 1998

Fingerprint

Hamiltonians
Hamiltonian Dynamics
Distribution functions
Dynamical systems
Curvilinear Coordinates
Euclidean geometry
Geodesic Flow
Geometry
spherical coordinates
biology
System Dynamics
embedding
Biology
Euclidean space
Phase Space
Distribution Function
distribution functions
formalism
Arbitrary
geometry

Keywords

  • Darwin systems
  • Hamiltonian formalism
  • Population dynamics

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Hamiltonian dynamics of Darwin systems. / Shapovalov, A. V.; Evdokimov, E. V.

In: Physica D: Nonlinear Phenomena, Vol. 112, No. 3-4, 1998, p. 441-450.

Research output: Contribution to journalArticle

Shapovalov, AV & Evdokimov, EV 1998, 'Hamiltonian dynamics of Darwin systems', Physica D: Nonlinear Phenomena, vol. 112, no. 3-4, pp. 441-450.
Shapovalov, A. V. ; Evdokimov, E. V. / Hamiltonian dynamics of Darwin systems. In: Physica D: Nonlinear Phenomena. 1998 ; Vol. 112, No. 3-4. pp. 441-450.
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