Second order diagonal recurrent neural network

The model structure of the SDRNN have been shown in the attached image, second-order nonlinear system model is assumed as:

$$y(k+1)=\dfrac{y(k)y(k-1))[y(k)+4.5]}{1+y^2(k)+y^2(k-1)}+u(k).$$

The SDRNN(2, 7, 1) is used in simulation, that is, the input layer has 2 neurons $u(k)$ and $y(k)$, 7 neurons in hidden layer, 1 neuron $y(k +1)$ in output layer. The activation function is sigmoid function in hidden layer: this function is the commonly used bipolar function $\rho(x)=\dfrac{1-e^{-x}}{1+e^{-x}}$, initial weight is random value between -1 and 1, the learning rate $\eta=0.45$, momentum factorγ = 0.1.