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Integrability aspects of the dynamical forest model
Sulaiman, Evan
Amen, Azad
Aziz, Waleed
2023
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e-ISSN
2464-8728
Abstract
In this paper, we study the integrability problem of a mathematical models of forests with two age classes of the form, ẋ =ρy − (y − 1)²x − sx, ẏ = x − hy, where ρ, h, s ∈ R. We proved that the system has a unique Darboux polynomial if and only if ρ = 0. The model has only two or three exponential factors if h ≠ 0 or h = 0, respectively. It is also, showed that the system admits a Darboux first integral if and only if ρ = h = 0 and has no analytic first integral in any neighborhood of fixed point except when ρ = h = 0.
Source
Evan Sulaiman, Azad Amen, Waleed Aziz, "Integrability aspects of the dynamical forest model" in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.55 (2023)", EUT Edizioni Università di Trieste, Trieste, 2023, pp. 45-71
Languages
en
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