### 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 language | English |
---|---|

Pages (from-to) | 441-450 |

Number of pages | 10 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 112 |

Issue number | 3-4 |

Publication status | Published - 1998 |

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### Keywords

- Darwin systems
- Hamiltonian formalism
- Population dynamics

### ASJC Scopus subject areas

- Applied Mathematics
- Statistical and Nonlinear Physics

### Cite this

*Physica D: Nonlinear Phenomena*,

*112*(3-4), 441-450.

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

Research output: Contribution to journal › Article

*Physica D: Nonlinear Phenomena*, vol. 112, no. 3-4, pp. 441-450.

}

TY - JOUR

T1 - Hamiltonian dynamics of Darwin systems

AU - Shapovalov, A. V.

AU - Evdokimov, E. V.

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

KW - Darwin systems

KW - Hamiltonian formalism

KW - Population dynamics

UR - http://www.scopus.com/inward/record.url?scp=0039842024&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039842024&partnerID=8YFLogxK

M3 - Article

VL - 112

SP - 441

EP - 450

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 3-4

ER -