From a computational point of view, in nonlinear dynamical systems, attractors can be
regarded as self-excited and hidden attractors. Self-excited attractors can be localized …

The aim of this paper is to share with the mathematical community a list of 33 problems that I
have found along the years in my research. I believe that it is worth to think about them and …

We give a complete algebraic characterization of the first integrals of the Rayleigh–Duffing
oscillator. We prove the non existence of centers of such system and we study the form of the …

In this paper we determine the centers of quasi-homogeneous polynomial planar vector
fields of degree 0, 1, 2, 3 and 4. In addition, in every case we make a study of the reversibility …

In this paper we study planar polynomial differential systems of this form: where A, B∈ Z [X,
Y] and degA≤ d, degB≤ d,‖ A‖∞≤ H and‖ B‖∞≤ H. A lot of properties of planar …

This paper is devoted to the study of limit cycles that can bifurcate of a perturbation of
piecewise non-Hamiltonian systems with nonlinear switching manifold. We derive the first …

Symmetries and Semi-invariants in the Analysis of Nonlinear Systems details the analysis of
continuous-and discrete-time dynamical systems described by differential and difference …

Our work is concerned with the number of limit cycles and isochronous center conditions for
a class of three-dimensional cubic Kolmogorov systems with an equilibrium point in the …

In the present work the methods of computation of Lyapunov quantities and localization of
limit cycles are demonstrated. These methods are applied to investigation of quadratic …

In this paper we study the existence of nonlinear oscillations of a modified Leslie–Gower
model around the positive equilibrium point. It is proved that at least one limit cycle can exist …