Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.55 (2023)

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Madani Douib
Existence and exponential decay of solutions for magnetic effected piezoelectric beams with second sound and distributed delay term

Sujoy Majumder, Debabrata Pramanik
On meromorphic solutions of a certain type of nonlinear differential-difference equation

Evan Sulaiman, Azad Amen, Waleed Aziz
Integrability aspects of the dynamical forest model

Sylvain Mallot
One-ended 3-manifolds without locally finite toric decompositions

Benjamin Cahen
Complex Weyl symbols of metaplectic operators: An elementary approach

Bertrand Eynard, Danili Lewański
A natural basis for intersection numbers

Houssam Boukhecham, Hamza Ounesli
Topology of the space of measure-preserving transformations of the circle

Asit Kumar Chongdar, Amartya Chongdar, Sushanta Kumar Mohanta
On generating functions of extended Jacobi polynomials

Giovanni Vidossich
Three general uniqueness theorems for BVPs of ODEs with applications

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Integrability aspects of the dynamical forest model
(2023)
Sulaiman, Evan
;
Amen, Azad
;
Aziz, Waleed
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.
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