In this paper, the circular system of Riccati type complex difference equations of the form

$$u_{n+1}^{(j)}=\frac{a_j{u}_n^{(j-1)}+b_j}{c_j{u}_n^{(j-1)}+d_j},n=0,1,2,\cdots ,j=1,2,\cdots ,k,$$

where $u_n^{(0)}:=u_n^{(k)}$ for all $n$, is investigated. First, the forbidden set of the equation is given. Then the solvability of the system is examined and the expression of the solutions, given in terms of their initial values. Next, the asymptotic behaviour of the solutions is studied. Finally, in case of negative Riccati real numbers

$$R_j:=\frac{a_j{d}_j-b_j{c}_j}{[a_j+d_j{]}^2},j\in \overline{1,k},$$

it is shown that there exists a unique positive fixed point which attracts all solutions starting from positive states.

In ^[24], E. Tasdemir, et al. proved that the positive equilibrium of the nonlinear discrete equation $x_{n+1}=1+p\frac{x_{n-m}}{x_n^2}$ is globally asymptotically stable for $p\in (0,\frac{1}{2})$, {locally} asymptotically stable for $p\in (\frac{1}{2},\frac{3}{4})$ and it was { conjectured} that for any $p$ in the open interval $(\frac{1}{2},\frac{3}{4})$ the equilibrium is { globally} asymptotically stable. In this paper, we prove that this conjecture is true for the closed interval $[\frac{1}{2},\frac{3}{4}].$ In addition, it is shown that for $p\in (\frac{3}{4},1)$ the behaviour of the solutions depend on the delay $m.$ Indeed, here we show that in case $m=1$, there is an unstable equilibrium and an asymptotically stable 2-periodic solution. But, in case $m=2$, there is an asymptotically stable equilibrium. These results are obtained by using linearisation, a method lying on the well known Perron's stability theorem (^[17], p. 18). Finally, a conjecture is posed about the behaviour of the solutions for $m>2$ and $p\in (\frac{3}{4},1)$.