Dynamics of two classes of recursive sequences

We investigate the dynamics of two classes of recursive sequences: xn+1=∑j=0k∑(i0,i1,…,i2j)∈A2jxn−i0xn−i1⋯xn−i2j+b∑j=1k∑(i0,i1,…,i2j−1)∈A2j−1xn−i0xn−i1⋯xn−i2j−1+1+b, and xn+1=∑j=1k∑(i0,i1,…,i2j−1)∈A2j−1xn−i0xn−i1⋯xn−i2j−1+1+b∑j=0k∑(i0,i1,…,i2j)∈A2jxn−i0xn−i1⋯xn−i2j+b. We prove that their unique equilibrium x¯=1 is globally asymptotically stable. In addition, a new approach is presented to research the theory of recursive sequences.