Abstract This paper presents an analysis of lower bounds on local criticality within the family of piecewise quadratic reversible centers. Through a study of perturbations within this class, we determine that a minimum of five (in the linear case) or four (in the nonlinear case) local critical periods can bifurcate from the isochronous center. Notably, five represents the highest level of weakness observed in this context.
Rezende et al. (Sun,) studied this question.