73 citations · 353 across the 19 of their papers we have counts for
20 papers
Integrability and solvability of polynomial Liénard differential systems
Maria V. Demina
We provide the necessary and sufficient conditions of Liouvillian integrability for Liénard differential systems describing nonlinear oscillators with a polynomial damping and a po…
The method of Puiseux series and invariant algebraic curves
Maria V. Demina
An explicit expression for the cofactor related to an irreducible invariant algebraic curve of a polynomial dynamical system in the plane is derived. A sufficient condition for a p…
Invariant algebraic curves for Liénard dynamical systems revisited
Maria Demina
A novel algebraic method for finding invariant algebraic curves for a polynomial vector field in is introduced. The structure of irreducible invariant algebraic curv…
From Puiseux series to invariant algebraic curves: the FitzHugh-Nagumo model
Maria V. Demina
A relationship between Puiseux series satisfying an ordinary differential equation corresponding to a polynomial dynamical system and degrees of irreducible invariant algebraic cur…
Multi-particle dynamical systems and polynomials
Maria V. Demina, Nikolai A. Kudryashov
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding p…
Elliptic solutions in the Hénon - Heiles model
Maria V. Demina, Nikolai A. Kudryashov
Equations of motion corresponding to the Hénon - Heiles system are considered. A method enabling one to find all elliptic solutions of an autonomous ordinary differential equation…