# The five-variable Volterra system

Open Mathematics (2011)

- Volume: 9, Issue: 4, page 888-896
- ISSN: 2391-5455

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topJanusz Zieliński. "The five-variable Volterra system." Open Mathematics 9.4 (2011): 888-896. <http://eudml.org/doc/269519>.

@article{JanuszZieliński2011,

abstract = {We give a description of all polynomial constants of the five-variable Volterra derivation, hence of all polynomial first integrals of its corresponding Volterra system of differential equations. The Volterra system plays a significant role in plasma physics and population biology.},

author = {Janusz Zieliński},

journal = {Open Mathematics},

keywords = {Volterra derivation; Lotka-Volterra derivation; Polynomial constant; Polynomial first integral; first integral; Volterra dynamical system},

language = {eng},

number = {4},

pages = {888-896},

title = {The five-variable Volterra system},

url = {http://eudml.org/doc/269519},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Janusz Zieliński

TI - The five-variable Volterra system

JO - Open Mathematics

PY - 2011

VL - 9

IS - 4

SP - 888

EP - 896

AB - We give a description of all polynomial constants of the five-variable Volterra derivation, hence of all polynomial first integrals of its corresponding Volterra system of differential equations. The Volterra system plays a significant role in plasma physics and population biology.

LA - eng

KW - Volterra derivation; Lotka-Volterra derivation; Polynomial constant; Polynomial first integral; first integral; Volterra dynamical system

UR - http://eudml.org/doc/269519

ER -

## References

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- [9] Nowicki A., A factorisable derivation of polynomial rings in n variables (in press) Zbl1273.13048
- [10] Nowicki A., Zieliński J., Rational constants of monomial derivations, J. Algebra, 2006, 302(1), 387–418 http://dx.doi.org/10.1016/j.jalgebra.2006.02.034 Zbl1119.13021
- [11] Ossowski P., Zieliński J., Polynomial algebra of constants of the four variable Lotka-Volterra system, Colloq. Math., 2010, 120(2), 299–309 http://dx.doi.org/10.4064/cm120-2-9 Zbl1207.13016
- [12] Zieliński J., Factorizable derivations and ideals of relations, Comm. Algebra, 2007, 35(3), 983–997 http://dx.doi.org/10.1080/00927870601117639 Zbl1171.13013

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