Quadratic perturbations of a quadratic reversible Lotka-Volterra system (Q611140)

Perturbed Lotka-Volterra differential system of the form \[ \dot{x}=-y+x^2-y^2+\varepsilon (a_0+a_1x+a_2y+a_3x^2+a_4xy+a_5y^2), \] \[ \dot{y}=x+2xy+\varepsilon (b_0+b_1x+b_2y+b_3x^2+b_4xy+b_5y^2), \] are investigated in order to detect the configuration of limit cycles. The results are obtained via averaging theory.