Stability of the Gumowski-Mira equation with period-two coefficient

We investigate the stability of solutions of the Gumowski-Mira equation with a period-two coefficient: yn+1=ynbn+yn2−yn−1,n=0,1,…,withbn={α⩾0for n=2k,β⩾0for n=2k+1,k=0,1,…, and the initial values y−1,y0 are real numbers.