Chaos in rational systems in the plane containing quadratic terms

Consider the following system of rational equations containing quadratic terms x n + 1 = A 1 x n 2 + B 1 x n y n + C 1 y n 2 + D 1 x n + E 1 y n + F 1 α 1 x n 2 + β 1 x n y n + γ 1 y n 2 + λ 1 x n + μ 1 y n + ν 1 , y n + 1 = A 2 x n 2 + B 2 x n y n + C 2 y n 2 + D 2 x n + E 2 y n + F 2 α 2 x n 2 + β 2 x n y n + γ 2 y n 2 + λ 2 x n + μ 2 y n + ν 2 . 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 F 1 = F 2 = 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.