The period function in a class of quadratic Kolmogoroff systems

Marco Uribe S., Myrna Wallace C.


In this paper we consider the family of quadratic Kolmogoroff systems with a center in the real quadrant:

where 1 < a < ∞:This system has three invariant lines (the coordinate axes and the line x + y - 1 = 0) and a family of periodic solutions nested around a center and filling out the triangle determined by the three invariant lines. Using integrability of this system we reduce the abelian integral representing the period function and its derivative. The main result is that the corresponding period function is monotone increasing for values of the parameter near a = 3.

Palabras clave

Invariants; period functions; invariantes; funciones periódicas.

Texto completo:



Chicone C. and Jacob M. Bifurcation of critical periods for plane vector fields. Trans. Amer. Math. Soc. 312, N 12, (1989).

Chicone C. The monotonicity of period function for planar hamiltonian vector fields. Journal of Differential Equation 69, (1987).

Gasull A., Guillamon A. and Mañosa V. An expression for the first Liapunov and period constants with application. Preprint, Universidad Autonoma de Barcelona, España.

Gasull A., Guillamon A. and Mañosa V. Center and Isochronicity conditions for systems with homogeneus nonlinearities. Proceeding of the 2a catalan days on applied mathematics. (1995).

Van Horssen W and Reyn J. Bifurcation of limit cycles in a particular class of quadratic systems. Differential and Integral Equation Vol. 8 , N 4, (1995).


Enlaces refback

  • No hay ningún enlace refback.