A quadratic system with a nonmonotonic period function

Abstract

For a certain c ∗ > 1.4 {c_ * } > 1.4 and c ∈ ( 1.4 , c ∗ ) c \in \left ( {1.4,{c_ * }} \right ) the quadratic system x ˙ = − y + x y , y ˙ = x + 2 y 2 − c x 2 \dot x = - y + xy,\dot y = x + 2{y^2} - c{x^2} has a center at the origin surrounded by a one-parameter family of periodic trajectories. We show the period is not a monotone function of the parameter.