# Asymptotic behaviour of a discrete dynamical system generated by a simple evolutionary process

International Journal of Applied Mathematics and Computer Science (2004)

- Volume: 14, Issue: 1, page 79-90
- ISSN: 1641-876X

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topKarcz-Dulęba, Iwona. "Asymptotic behaviour of a discrete dynamical system generated by a simple evolutionary process." International Journal of Applied Mathematics and Computer Science 14.1 (2004): 79-90. <http://eudml.org/doc/207682>.

@article{Karcz2004,

abstract = {A simple model of phenotypic evolution is introduced and analysed in a space of population states. The expected values of the population states generate a discrete dynamical system. The asymptotic behaviour of the system is studied with the use of classical tools of dynamical systems. The number, location and stability of fixed points of the system depend on parameters of a fitness function and the parameters of the evolutionary process itself. The influence of evolutionary process parameters on the stability of the fixed points is discussed. For large values of the standard deviation of mutation, fixed points become unstable and periodical orbits arise. An analysis of the periodical orbits is presented.},

author = {Karcz-Dulęba, Iwona},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {asymptotic behaviour; phenotypic evolution; small populations; population dynamics; space of population states},

language = {eng},

number = {1},

pages = {79-90},

title = {Asymptotic behaviour of a discrete dynamical system generated by a simple evolutionary process},

url = {http://eudml.org/doc/207682},

volume = {14},

year = {2004},

}

TY - JOUR

AU - Karcz-Dulęba, Iwona

TI - Asymptotic behaviour of a discrete dynamical system generated by a simple evolutionary process

JO - International Journal of Applied Mathematics and Computer Science

PY - 2004

VL - 14

IS - 1

SP - 79

EP - 90

AB - A simple model of phenotypic evolution is introduced and analysed in a space of population states. The expected values of the population states generate a discrete dynamical system. The asymptotic behaviour of the system is studied with the use of classical tools of dynamical systems. The number, location and stability of fixed points of the system depend on parameters of a fitness function and the parameters of the evolutionary process itself. The influence of evolutionary process parameters on the stability of the fixed points is discussed. For large values of the standard deviation of mutation, fixed points become unstable and periodical orbits arise. An analysis of the periodical orbits is presented.

LA - eng

KW - asymptotic behaviour; phenotypic evolution; small populations; population dynamics; space of population states

UR - http://eudml.org/doc/207682

ER -

## References

top- Chorążyczewski A., Galar R. and Karcz-Dulęba I. (2000): Considering phenotypic evolution in the space of population states.- Proc. 5th Int. Conf. Neural Networks and Soft Computing, Zakopane, Poland, pp. 615-620.
- Dulęba I. and Karcz-Dulęba I. (1996): The analysis of discrete dynamical system generated by some evolutionary process. - Proc. IX Symp. Simulation of Dynamical Processes, Zakopane, Poland, pp. 351-356, (in Polish). Zbl1171.92333
- Galar R. (1985): Handicapped individua in evolutionary processes. - Biol. Cybern., Vol. 51, No. 1, pp. 1-9. Zbl0566.92013
- Galar R. and Karcz-Dulęba I. (1994): The evolution of two: An example of space of states approach. - Proc. 3rd Annual Conf. Evolutionary Programming, San Diego CA: World Scientific, pp. 261-268.
- Karcz-Dulęba I. (2000): Dynamics of evolution of population of two in the space of population states. The case of symmetrical fitness functions. - Proc. 4th Nat. Conf. Evolutionary Algorithms and Global Optimization, Lądek Zdrój, pp. 115-122 (in Polish).
- Karcz-Dulęba I. (2002a): Evolution of a two-element population in the space of population states: Equilibrium states for asymmetrical fitness functions, In: Evolutionary Algorithms and Global Optimization (J. Arabas Ed.). - Warsaw: Warsaw University of Technology Press, pp. 35-46.
- Karcz-Dulęba I. (2002b): Domains of attraction of dynamical system generated by simple evolutionary model. - Proc. Workshop on Genetic Algorithms, Bielsko-Biała - Szyndzielnia, Poland, pp. 20-22, (in Polish).
- Vose M.D. (1999): The Simple Genetic Algorithm. Foundations and Theory. - Cambridge: The MIT Press. Zbl0952.65048

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