Chaos in rational systems in the plane containing quadratic terms

Consider the following system of rational equations containing quadratic termsxn+1=A1xn2+B1xnyn+C1yn2+D1xn+E1yn+F1α1xn2+β1xnyn+γ1yn2+λ1xn+μ1yn+ν1,yn+1=A2xn2+B2xnyn+C2yn2+D2xn+E2yn+F2α2xn2+β2xnyn+γ2yn2+λ2xn+μ2yn+ν2.Chaos in the sense of Li–Yorke is considered. This is based on the Marotto’s theorem via obtaining a snap-back repeller. In fact, first in a special case when F1=F2=0F1=F2=0, we show that origin is a snap-back repeller and so the system has chaotic behavior in the sense of Li–Yorke under some conditions. Then in a more general case, we prove that existence of chaos in the sense of Li–Yorke for the above system.