This paper is devoted to study the algebraic limit cycles of planar piecewise linear differential systems. In particular, we present examples exhibiting two explicit hyperbolic algebraic limit cycles, as well as some ...

In this paper we study the action of planar birational transformations, also known as plane Cremona maps, on quadratic planar differential systems. We provide geometrical characterizations of when a quadratic system is ...

In this paper, we give the normal form of all planar polynomial vector fields of degree d ≤ 3 having two nonconcentric circles C1 and C2 as invariant algebraic curves and the function H=Cβ 1 Cα 2, with α and β real values, ...

We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of cubic polynomial differential centers when it is perturbed inside the class ...

Neste trabalho fazemos o estudo de uma classe de sistemas diferenciais polinomiais quadráticos definidos em R3 que possui um cilindro como superfície algébrica invariante. Mais especificamente, fizemos o estudo da estabilidade ...

We consider a piecewise smooth vector field in R3, where the switching set is on an algebraic variety expressed as the zero of a Morse function.We depart from a model described by piecewise constant vector fields with a ...

In this paper, we perform a global analysis of the dynamics of the Chen system(x) over dot = a(y - x), (y) over dot = (c - a)x - xz + cy, (z) over dot = xy - bz,where (x, y, z) is an element of R-3 and (a, b, c) is an ...

Invariant algebraic surfaces are commonly observed in differential systems arising in mathematical modeling of natural phenomena. In this paper, we study the integrability and dynamics of quadratic polynomial differential ...